If X is a random variable such that E(X)=3 and V(X)=2, and if Y is a...

Question

Question

If X is a random variable such that E(X)=3 and V(X)=2, and if Y is a random variable such that Y=6+2X. Calculate the mean and variance of Y.

a) E(Y)=12

b) V(Y)=

math Statistics-And-Probability

Answer 1

Answer #1

we want to find V(Y)

given value E(X)=3 V(X)=2

Y=6+2X.

V(Y)=V(6+2*x) = 2^2 * V(x) = 4*2 = 8 ( we know the constant of variance is zero)

Answer 2

Similar Homework Help Questions

Let the variance of random variable X be 3, the variance of Y be 12, and...

Let the variance of random variable X be 3, the variance of Y be 12, and the variance of Z be 9, and let X, Y , and Z be uncorrelated. Find V ar(4 − 2X + 3Y − 10Z).
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) =...
Let X be a random variable with E(X) = µ and V (X) = σ 2...

Let X be a random variable with E(X) = µ and V (X) = σ 2 . Let a and b be constants (fixed numbers) and define another random variable Y = aX + b. Find the E[Y ] and V [Y ] in terms of E(X) = µ and V (X) = σ 2 . From your results, tell whether adding or subtracting a constant to the random variable changes its variance.

3Y 2 1. (20 points) Suppose that X and Y independent random variables. Let W 2x (a) Consider the following probability...

3Y 2 1. (20 points) Suppose that X and Y independent random variables. Let W 2x (a) Consider the following probability distribution of a discrete random variable X: 12 P(X) 00.7 0.3 X Compute the mean and variance of X (b) Use your answers in part (a). If E(Y)=-3 and V(Y)= 1, what are E(W) and V (W)?
can you solve 1 and 2 please??? 1. Calculate E(Y) and SD(Y) for the random variable...

can you solve 1 and 2 please??? 1. Calculate E(Y) and SD(Y) for the random variable Y with pdf gy (y) = -7?, 1<y<4. 2. The random variable X has mean jix = 12 and standard deviation o x = 5. Define a new random variable Y = ax + b. (a) Calculate My and oy when a = -2 and 6 -3. (b) Calculate the values of a and b that result in My = 20 and a 100.
Assume X is a normal random variable with mean 20 and variance 16, and Y is a Gamma random variable with parameters 5 a...

Assume X is a normal random variable with mean 20 and variance 16, and Y is a Gamma random variable with parameters 5 and 2. In addition X and Y are independent. Construct a box with length L = [X], width W = 2|X|, and height H = Y. Let V be the volume of the box. Calculate the expected value E[V]?

5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider...

5. Suppose X is a normally distributed random variable with mean μ and variance 2. Consider a new random variable, W=2X + 3. i. What is E(W)? ii. What is Var(W)? 6. Suppose the random variables X and Y are jointly distributed. Define a new random variable, W=2X+3Y. i. What is Var(W)? ii. What is Var(W) if X and Y are independent?
X is exponential random variable with λ = 3. A) Calculate E(X"2) of this random variable....

X is exponential random variable with λ = 3. A) Calculate E(X"2) of this random variable. B) Calculate V(X 2)
7. X is a random variable with a mean of 2 and a variance of 3,...

7. X is a random variable with a mean of 2 and a variance of 3, and Y is a random variable with a mean of 4 and a variance of 5, and the covariance between X and Y is -3. Define (a) Find the expected value of W. b) Find the variance of W

9. The random variable x is distributed normally with mean Mx. and variance 6 and random...

9. The random variable x is distributed normally with mean Mx. and variance 6 and random Variable Y is normally distributed with mean & and Variance or 2x=34 is distributed hormally with mean 12 and variance 42 Assume Independence Find values Ux and by. Possible answers: Mx = 18 & Gyr by=va mx-128 6y=842 My 686y=2 ty=-68