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Q1. [4 marks Find the expectation and standard deviation of the uniform random variable X that...
A value=2 A -2 It is known that for a random variable X, the Expectation of...
A value=2
A -2 It is known that for a random variable X, the Expectation of X equals 5, and that the Variance equals 7. A random variable Y is defined as: Y= AX+2A = (INSERT THE VALUE OF A) 3(a) Find the Expectation of Y 3(b) Find the Variance of Y 3(c) Find E[Y) 3(d) Find the Standard Deviation of Y Question 4 (10%) For the following probability density function. What is the probability P(x>0.? SÅ (1-x) -A<x<A
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean...
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean and variance of X. (2) Let Y 2X+3. Draw the PDF of Y [8 marks] 6 marks] [8 marks (3) Find the mean and variance of Y
4. Standard deviation and risk. The standard deviation o(X) of a random variable is the square...
4. Standard deviation and risk. The standard deviation o(X) of a random variable is the square root of the variance that is o(X) = Var(X). It characterizes the "spread" of the random variable X. If a random variable X has expected value p and standard deviation o, then X takes values which are on average at distance o from u. Imagine you have the choice to invest in two stock funds: an American fund with a rate return X and...
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean...
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) = .8, find Cov(2x-Y, X + 5Y).
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) =...
Find the mean, variance and standard deviation for the random variable X: Random Variable X -2...
Find the mean, variance and standard deviation for the random variable X: Random Variable X -2 1 3 P(X = x) 0.1 0.3 .6 Show the calculations that you need for each part. You will get no credit for using your calculator or Excel and only giving the answer. You should write out: mean = ........ (show how the mean is calculated) Vairance = .............. Standard Deviation = ................
Between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
Between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
A Normal random variable X has mean 20 and standard deviation 4. Calculate the probability that...
A Normal random variable X has mean 20 and standard deviation 4. Calculate the probability that specific values of X exceed 26. Calculate the 36th percentile of a Standard Normal random variable. A Standard Normal random variable Z falls within an interval of values centered around zero, that is the interval -z to z, with probability 0.6. Calculate the value of z that defines that interval. A truck makes daily round trips between Charlotte and Atlanta. On 30 percent of...
Let X be a random variable with mean 6 and standard deviation 4. If L =...
Let X be a random variable with mean 6 and standard deviation 4. If L = 8-3X what is the standard deviation of L?
Answer the following questions: (a) Suppose X is a uniform random variable with values 1, 2,...
Answer the following questions: (a) Suppose X is a uniform random variable with values 1, 2, 3, and 4. Then, 1) P(X = 3) = (correct to 2 decimal). 2) P(X S 3) = (correct to 2 decimal) 3) P(X > 3) = (correct to 2 decimal) 4) P(2 < X < 4) = (correct to 1 decimal) (b) Suppose Y is a random variable having Binomial distribution with parameters n = 10 and p = 0.5. Find (1) P(Y...
A value=2
A -2 It is known that for a random variable X, the Expectation of X equals 5, and that the Variance equals 7. A random variable Y is defined as: Y= AX+2A = (INSERT THE VALUE OF A) 3(a) Find the Expectation of Y 3(b) Find the Variance of Y 3(c) Find E[Y) 3(d) Find the Standard Deviation of Y Question 4 (10%) For the following probability density function. What is the probability P(x>0.? SÅ (1-x) -A<x<A
Q1. Let X be a random variable uniformly distributed over [-2, 4] (1) Find the mean and variance of X. (2) Let Y 2X+3. Draw the PDF of Y [8 marks] 6 marks] [8 marks (3) Find the mean and variance of Y
4. Standard deviation and risk. The standard deviation o(X) of a random variable is the square root of the variance that is o(X) = Var(X). It characterizes the "spread" of the random variable X. If a random variable X has expected value p and standard deviation o, then X takes values which are on average at distance o from u. Imagine you have the choice to invest in two stock funds: an American fund with a rate return X and...
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) = .8, find Cov(2x-Y, X + 5Y).
If X is a random variable with mean -3 and standard deviation 2, Y is a random variable with mean 5 and standard deviation 3, and the correlation between X and Y is ρ Corr(X, Y) =...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
Answer the following questions: (a) Suppose X is a uniform random variable with values 1, 2, 3, and 4. Then, 1) P(X = 3) = (correct to 2 decimal). 2) P(X S 3) = (correct to 2 decimal) 3) P(X > 3) = (correct to 2 decimal) 4) P(2 < X < 4) = (correct to 1 decimal) (b) Suppose Y is a random variable having Binomial distribution with parameters n = 10 and p = 0.5. Find (1) P(Y...
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