The mean function of the random process. X(t) is:μ(t) = E[X(t)] = (1/3) [sin (4πt + 2Ө) - sin (2πt + Ө)].
Given X(t) = A cos(wet + Ө), where the amplitude A is a uniformly distributed random variable over (-1, 2), while the phase Ө and the frequency we are constants.
To calculate the mean function of the random process, we know that the mean is defined as E[X(t)].
Therefore, E[X(t)] = E[A cos(wet + Ө)]
We know that A is uniformly distributed over (-1,2).
The probability density function of a uniform distribution over (a, b) is f(x) = 1/(b - a) if a ≤ x ≤ b and 0 otherwise.
Using this probability density function, the mean of A is given by E[A] = (2 + (-1))/2 = 0.5.
We can apply the Law of Total Probability to calculate E[X(t)] as follows:
E[X(t)] = E[A cos (wet + Ө)] = ∫cos (wet + Ө) f(A) dA (from -1 to 2) = ∫cos (wet + Ө) (1/3) dA (from -1 to 2) = (1/3) [sin (2wet + 2Ө) - sin (wet + Ө)] (from -1 to 2) = (1/3) [sin (4πt + 2Ө) - sin (2πt + Ө)].
Therefore, the mean function of X(t) is:μ(t) = E[X(t)] = (1/3) [sin (4πt + 2Ө) - sin (2πt + Ө)].
We can find the autocorrelation function of X(t) as follows: R (t1, t2) = E[X(t1) X(t2)] = E[A cos (wet1 + Ө)A cos (wet2 + Ө)].
The product of two cosine functions can be written in terms of the sum of the cosine and sine functions as follows: cos(x)cos(y) = (1/2)[cos (x + y) + cos (x - y)] sin (x)sin(y) = (1/2) [cos (x - y) - cos (x + y)]
Therefore, A cos (wet1 + Ө)A cos (wet2 + Ө) = (1/2)A² [cos (wet1 + wet2 + 2Ө) + cos (wet1 - wet2)] + (1/2)A² [cos (wet1 - wet2) - cos (wet1 + wet2 + 2Ө)]
We can find the expected value of this expression as follows: E[A cos(wet1 + Ө)A cos(wet2 + Ө)] = (1/2)E[A²] [cos(wet1 + wet2 + 2Ө) + cos(wet1 - wet2)] + (1/2)E[A²] [cos(wet1 - wet2) - cos(wet1 + wet2 + 2Ө)] = (1/3) [cos(wet1 + wet2 + 2Ө) + cos(wet1 - wet2)]
Therefore, R(t1, t2) = E[X(t1) X(t2)] = (1/3) [cos (wet1 + wet2 + 2Ө) + cos (wet1 - wet2)]
Therefore, X(t) is wide-sense stationary, as the mean function and autocorrelation function depend only on the time difference t1 - t2, and not on the absolute values of t1 and t2.
To know more about mean function, visit:
https://brainly.com/question/32490353
#SPJ11
A number is multiplied by 6 and the result is 48. Find the number.
Answer:
the answer is 8
Step-by-step explanation:
8x6=48
Answer:
8
Step-by-step explanation:
its 8 because the multiples of 6 are 6, 12, 18, 24, 30, 36, 48 then the multiples of 8 are 8, 16, 24, 32, 40, 48
A principal was buying T-shirts for his school's math club and found that the total cost
in dollars could be found by the function f(x) = 9x + 7, where x is the number of
members in the club. If there are at least 12 members on the team but not more than
16, then which of the following statements describes the function?
A. The value of x must be a whole number between 12 and 16 and the value of f(x)
must be a whole number between 9 and 7.
B. The value of x must be a whole number between 12 and 16 and the value of f(x)
must be a whole number between 115 and 151.
C. The value of x must be a whole number between 0 and 16 and the value of f(x) must
be a whole number between 0 and 151.
D. The values of x and f(x) must both be whole numbers between 7 and 9.
Answer: B, makes the most sence
Step-by-step explanation:
0.8x + ⅕ = 6/10x - 6 - 4
i need to figure out the variable
Answer:
x = -51
Step-by-step explanation:
Do I need to explain oorrrrrrrrr.....
15,23,31,39, find the 60th term
Answer:
487
Step-by-step explanation:
We can use this formula to find the 60th term:
8n+7
Had 2 pages of algebra ! :C my brain is not working anymore..
Step-by-step explanation:
given,
[tex]2k \div 3 = 6 \\ 2k \div3 \times 3 = 6 \times 3 \\ 2k = 18 \\ k = 18 \div 2 \\ = 9[/tex]
Please answer this onee :C
Answer:
1
Step-by-step explanation:
Answer:
A) 1
Step-by-step explanation:
The number 1 was spun the fewest times. We know this because there is only one x above the 1, suggesting it wa spun the fewest times.
Hope it helps!!!
Greece has faced a severe economic crisis since the end of 2009. A social science researcher claims that 25% of all Greeks who would rate their lives poorly enough to be considered "suffering". To test this claim, a Gallup poll decides to survey 1,000 randomly sampled Greeks and record P. the proportion of Greeks from this sample who would rate their lives poorly enough to be considered "suffering".
a) Describe the population parameter of interest.
b) Check if the success-failure condition required for the Central Limit Theorem for the sample proportion is met.
c) What is the sampling distribution of p if the social science researcher's claim is correct?
d) What is the probability that the sample proportion p is between 24% and 28% if the social science researcher's claim is correct?
The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered "suffering."b) The success-failure condition is met.c) The sampling distribution of p is a normal distribution with a mean equal to the population proportion and a standard deviation given by the formula σp = sqrt[p(1−p)/n]. If we assume that the claim is true, then p = 0.25, and the sample size is 1000, and hence the standard deviation of the sampling distribution of p is: sqrt[p(1−p)/n] = sqrt[(0.25)(0.75)/1000] ≈ 0.0144d) The probability that the sample proportion p is between 24% and 28% if the social science researcher's claim is correct is 0.6615 or 66.15% (approximately).
Population parameter of interest:The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered "suffering". The parameter of interest in this case is the percentage of Greeks who would be classified as "suffering."b) Check if the success-failure condition required for the Central Limit Theorem for the sample proportion is met.The success-failure condition is met when the number of successes and failures in the sample is both larger than 10. Let’s assume that the claim is true, thus the proportion p is equal to 0.25.
The sample size is 1,000. Therefore, the expected number of successes and failures arenp = 1,000 × 0.25 = 250n(1−p) = 1,000 × 0.75 = 750Both expected number of successes and failures are greater than 10, therefore, the success-failure condition is met.c) Sampling distribution of p if the social science researcher's claim is correct:The sampling distribution of p is a normal distribution with a mean equal to the population proportion and a standard deviation given by the formula σp = sqrt[p(1−p)/n]. If we assume that the claim is true, then p = 0.25, and the sample size is 1000, and hence the standard deviation of the sampling distribution of p is:sqrt[p(1−p)/n] = sqrt[(0.25)(0.75)/1000] ≈ 0.0144d) Probability that the sample proportion p is between 24% and 28% if the social science researcher's claim is correct:
The sample proportion, p, follows a normal distribution with mean 0.25 and standard deviation 0.0144. Therefore, the standardized value of 0.24 is(0.24−0.25)/0.0144 = -0.6944and the standardized value of 0.28 is(0.28−0.25)/0.0144 = 2.0833From standard normal distribution table, the probability of getting a value between -0.6944 and 2.0833 is approximately 0.6615. Thus, the probability that the sample proportion is between 24% and 28% is 0.6615 or 66.15% (approximately).
Answer: a) The population parameter of interest is the proportion of all Greeks who would rate their lives poorly enough to be considered "suffering."b) The success-failure condition is met.c) The sampling distribution of p is a normal distribution with a mean equal to the population proportion and a standard deviation given by the formula σp = sqrt[p(1−p)/n]. If we assume that the claim is true, then p = 0.25, and the sample size is 1000, and hence the standard deviation of the sampling distribution of p is: sqrt[p(1−p)/n] = sqrt[(0.25)(0.75)/1000] ≈ 0.0144d) The probability that the sample proportion p is between 24% and 28% if the social science researcher's claim is correct is 0.6615 or 66.15% (approximately).
Learn more about sampling distribution here:
https://brainly.com/question/31465269
#SPJ11
(Beautiful Mind) There is an interesting scene in A Beautiful Mind in which John Nash's character discovers his equilibrium concept. The setup is that there are four men and five women at a bar, and each man must simultaneously walk over to a woman. One of the women, who is blonde, is considered to be more desirable than the other four, who are all brunettes. Although the men all prefer the blonde to the brunettes, if they all go for the blonde they will "block each other" (according to the logic of the movie) and end up unsuccessful; moreover, after going for the blonde, they cannot then go to a brunette because the brunette would be offended at being someone's second choice and would turn down the man. Nash's character then realizes that what ought to happen is for each of the four men to choose a brunette. Let's try to put this situation in a game theoretic model by using a to denote the payoff a man would receive if another man goes for the same woman he does (here there are assumptions that it is possible to "block each other" on brunettes and that being "blocked" on a brunette gives the same payoff as being "blocked" on a blonde, although this is not important for the problem). We'll use b to refer to a man's payoff if he is the only man to go for a woman and that woman is a brunette. We'll use c to refer to a man's payoff if he is the only man to go for a woman and that woman is blonde. The natural restrictions on payoffs are a < b < c. Is there a pure strategy Nash equilibrium where each man ends up with a brunette? What are the pure strategy Nash equilbria? How do these answers change if the blonde turns down everyone (meaning that the payoff to going to the blonde is a, regardless of how many men choose her)? [Hint: classify situations based on how many men go to the blond woman.]
In the absence of the blonde turning down everyone, the pure strategy Nash equilibrium is for all men to choose brunettes. If the blonde turns down everyone, the pure strategy Nash equilibrium remains the same: all men choosing brunettes.
How to explain the Nash equillbriumIn this case, all four men choose brunettes. Since no man is going for the blonde, their payoff is b if they are the only man going for a brunette. This scenario is a pure strategy Nash equilibrium because no man has an incentive to deviate.
If one man goes for the blonde, his payoff is c. The other three men choose brunettes, resulting in a payoff of b. This situation is not a Nash equilibrium because the man going for the blonde has an incentive to deviate and choose a brunette instead, increasing his payoff to b.
Since the payoffs are the same for any number of men going for the blonde, the pure strategy Nash equilibrium is for all men to choose brunettes. Each man's payoff will be b, regardless of whether they choose the blonde or a brunette.
Learn more about Nash equillbrium
https://brainly.com/question/29398344
#SPJ1
i really need help. I don't understand
If f(x) is irreducible over R. then f(x²) is irreducible over R. True / False
The statement "If f(x) is irreducible over R, then f(x²) is irreducible over R" is false. The irreducibility of f(x) does not guarantee the irreducibility of f(x²) over R.
Does the irreducibility of f(x) over R imply the irreducibility of f(x²) over R? True / FalseThe statement "If f(x) is irreducible over R, then f(x²) is irreducible over R" is actually false. In other words, just because a polynomial, f(x), is irreducible over the real numbers (R), it does not necessarily mean that its square, f(x²), will also be irreducible over R.
To understand why, let's first clarify the concept of irreducibility.
A polynomial is considered irreducible if it cannot be factored into a product of two or more non-constant polynomials with coefficients in the same field. In this case, we are considering the field of real numbers (R).
Now, when we square a polynomial, such as f(x)² or f(x²), it can lead to changes in its factorization.
The squared polynomial may introduce new factors or change the multiplicity of existing factors.
This means that the irreducibility of the original polynomial, f(x), does not necessarily carry over to the squared polynomial, f(x²).
To illustrate this, let's consider an example. Suppose we have a polynomial f(x) = x² + 1, which is irreducible over R. If we square this polynomial, we get f(x²) = (x² + 1)² = x⁴ + 2x² + 1.
The squared polynomial, in this case, is no longer irreducible over R because it can be factored as (x² + 1)(x² + 1).
This example shows that the irreducibility of f(x) does not imply the irreducibility of f(x²). It's important to carefully analyze the specific factors and properties of each polynomial to determine its irreducibility.
Learn more about irreducibility
brainly.com/question/10724811
#SPJ11
Find the slope will give brainliest if it is correct.
Answer:
I cannot see pictures, so I will explain how to find slope, so you can do it on your own.
Step-by-step explanation:
Find 2 coordinates on the line.
Ex: (2,3) and (4,6)
Subtract the y-coords and x-coords from each other and divide.
6-3 = 3
4-2 = 2
3/2
So the example slope is 3/2.
The 3 represents the rise, and 2 represents the run.
---
hope it helps
What is the measure of ∠DBE?
Answer:
63 degree
Step-by-step explanation:
find the missing side round to the nearest tenth.
Answer:
Step-by-step explanation:
Remark
Cos(y) = adjacent Side / hypotenuse
y = 51 degrees
adjacent = 10
Solution
Cos(51) = 10/x Multiply both sides by x
x cos(51) = 10 Divide by Cos(51)
x = 10 / cos(51)
Cos(51) = .6293
x = 10/0.6293
x = 15.89
I do a two-way between-subjects ANOVA and find that my interaction F-test is significant. What do I do next?
If one of the effects is substantial, it should be included in the analysis as a control variable.
If none of the effects are important, the analysis may need to be redone with a more comprehensive model or a bigger sample size.
If you conduct a two-way between-subjects ANOVA and discover that the interaction F-test is important, the next thing to do is to interpret the results.
You may be interested in estimating the main effects of each variable and the interaction effect.
In a two-way ANOVA, a statistical method is employed to identify the interactions between two variables.
ANOVA stands for analysis of variance.
It is a statistical method used to compare two or more populations by analyzing the variance between them.
F-test is a statistical method used to compare two variances or to test hypotheses about whether two population variances are equal.
It can be used to compare more than two variances in ANOVA.
When the interaction effect in a two-way between-subjects ANOVA is important, the interpretation of the main effects of each variable and the interaction effect must be done.
If one of the effects is substantial, it should be included in the analysis as a control variable.
If none of the effects are important, the analysis may need to be redone with a more comprehensive model or a bigger sample size.
To know more about ANOVA, visit:
https://brainly.com/question/15084465
#SPJ11
given f(x) = x^4 – 3x^3 x – 3. what is limit of f (x) as x approaches negative 2?
A. –45
B. –13
C. 3
D. 35
After considering the given data we conclude that the evaluated limit of the given function is 35, which is option D
Here we have to apply the principle of evaluating function using a dedicated value.
Given [tex]f(x) = x^4 - 3x^3 x - 3,[/tex]we need to evaluate the limit of f(x) as x approaches negative 2.
To evaluate the limit, we can simply substitute x = -2 into the function:
[tex]f(-2) = (-2)^4 - 3(-2)^3(-2) - 3 = 16 + 24 - 2 - 3 = 35[/tex]
Therefore, the limit of f(x) as x approaches negative 2 is 35.
To learn more about function
https://brainly.com/question/29425948
#SPJ4
Can someone plz explain how to do this
Answer:
-2
Step-by-step explanation:
First, you need to find the equation.
f(x) = -3x + b
Now we need to find the y-intercept.
f(x) = -3x + b
f(-9) = -3(1) + b
-9 = -3 + b
-6 = b
f(x) = -3x - 6
The zero of f means that f(x) = 0
f(0) = -3x - 6
f(6) = -3x
x = -2
In which cases could comparing the observed and expected distributions help detect peculiarities in the data
1. A newly discovered secret novel from a deceased prolific author
2. The reported ages of users on a popular social networking site
3. Both of the above
4. None of the above
Comparing the observed and expected distributions can help detect peculiarities in the data in cases where there is an expectation or a known pattern that can be used for comparison.
A newly discovered secret novel from a deceased prolific author: In this case, comparing the observed distribution of the writing style, themes, or language in the novel with the expected distribution based on the author's previous works can help identify any peculiarities or deviations from the author's typical style.
The reported ages of users on a popular social networking site: Comparing the observed distribution of ages with the expected distribution based on demographic data or population statistics can reveal any anomalies or discrepancies, such as an unusually high or low frequency of certain age groups, which may indicate data inaccuracies or biases.
Both of the above: Both scenarios involve comparing observed and expected distributions to identify peculiarities or deviations in the data.
None of the above: If there is no expectation or known pattern to compare the observed distribution against, comparing the observed and expected distributions may not be applicable for detecting peculiarities in the data.
In conclusion, comparing observed and expected distributions can be helpful in detecting peculiarities in the data when there is an expectation or known pattern to use for comparison. It can be useful in scenarios such as analyzing a newly discovered novel from a deceased author or examining reported ages on a social networking site. However, if there is no expectation or known pattern, this method may not be applicable.
To know more about expected distributions refer here:
https://brainly.com/question/29210110
#SPJ11
Find the surface area of the following figure below. Use 3.14 for pi
Answer:
113.04
Step-by-step explanation:
Surface area for a sphere is 4*pi*radius^2
4*3*3*3.14
113.04
The surface area of the sphere with the given radius is 113.04cm².
SphereA sphere is simply a 3-dimensional object with no vertices and edges.
The surface area of a sphere is expressed as;
Area = 4πr²
Given the data in the question;
Radius of the sphere r = 3cmPie π = 3.14To determine the surface area of the sphere, we substitute our given values into the expression above.
Area = 4πr²
Area = 4 × 3.14 × (3cm)²
Area = 4 × 3.14 × 9cm²
Area = 113.04cm²
Therefore, the surface area of the sphere with the given radius is 113.04cm².
Learn more about area of sphere here: https://brainly.com/question/14692728
what is the the mode of April's temperatures?
A
B
C
D
Answer:
B: no mode
Explanation:
A mode is a number that occurs often in a set of data. Since all of April's temperatures are different, there is no mode.
Answer:
b because mode is the how many times a number pop up it has to be the same
Step-by-step explanation:
Matthew asked 10 students how many pets and how many siblings each has. The line plots below show his data. This is a x plot with xs
Complete question :
Matthew asked 10 students how many pets and how many siblings each has. The line plots below show his data.
Which statement correctly describes Matthew’s data?
A. The median number of pets the students have is less than the median number of siblings the students have.
B. There is less variability in the number of pets the students have than in the number of siblings the students have.
C. The range in the number of siblings the students have is less than the range in the number of pets the students have.
D. The mean absolute deviation of the number of siblings the students have is less than the mean absolute deviation of the number of pets the students have.
Answer:
B. There is less variability in the number of pets the students have than in the number of siblings the students have.
Step-by-step explanation:
From the data:
Pets data:
3,3,4,4,4,4,5,5,5,5
Using calculator:
Median value = 4
Mean absolute deviation = 0.64
Range = 5 - 3 = 2
Siblings data:
Median value = 2
Mean absolute deviation = 1.52
Range = 5 - 0 = 5
Median value of pets > median value of siblings data
Range of siblings data > range of pets data
Mean absolute deviation of siblings data >Ean absolute deviation of pets data
Variability of pets data is lesser than that of siblings data ; as shown by the mean absolute deviation value
hey guys i rlly need help i don't understand rational numbers
Answer:
if its not a fraction or a number that can be written as a fraction, its an irrational
pls pls help. i am begging u ill give brainliest
Answer:
4/18
Step-by-step explanation:
Help will brainlist 30 points!!!
Answer:
I believe it would be 5.
Step-by-step explanation:
I'm not completely sure, but this seems quite easy, so I hope I'm right :D
There are 6 different numbers on the number cube so x = 6
The 1/x means you have a 1 in x ( total choices) of getting a certain number.
The total choices would be the total numbers in the cube which is 6.
The answer is 6
Can anyone help with what the formula to calculate the volume of a Rhombohedron (3D Rhombus) is? Could you also give me an example of how to do it please?
Answer: the formula is : β = 180° - α
A = 6 * a² * sin(α)
V = a³ * (1-cos(α)) * √1+2cos(α)
Sorry, i don't know any examples .
Step-by-step explanation:
Oscar is drving 85 miles per hour. At this rate, how many miles will he drive in 2 1/2 hours?
Answer:
212.5 miles
Step-by-step explanation:
Which angles are neither obtuse angles nor acute angles?
Answer:
A right angle is neither Obtuse nor Acute
Step-by-step explanation:
Answer: Which angles are neither obtuse angles nor acute angles?
Write an equation that shows the relationship 64% of y is 40.
PLEASE HELP
Answer:
[tex]0.64*y = 40[/tex]
Step-by-step explanation:
Answer:
64/100=40/y
Step-by-step explanation:
We use the simple equation of finding percentages, which would be the percentage (64) over 100 percent, as this is our total. If 64 percent of y equals 40, then the equation is 64/100=40/y. To solve for y, multiply 100 x 40= 4000, then divide by 64 to get the answer. Y=62.5
solve eqn by factorisation method
2x squre-50x=0
Answer:
0 or 25
Step-by-step explanation:
To solve for x
we first factor
2x^2-50x=0
2x(x-25)=0
To make this equation 0 x has to be 0 or 25
I WILL GIVE BRAINLIEST!!!
consider the polynomial function q(x)=-2x^8+5x^6-3x^5+50
end behavior
Answer:
Step-by-step explanation:
ps. you can use m a t h w a y and check
it's spaced out cuz it doesn't let me write it well
100% of x is 50. *reamber is means divide*
Answer:
100% of 50 is 50
x = 50
Step-by-step explanation:
Answer:
x = 50
Remember that 100% of anything is the number itself.