Let X and Y be continuous random variables with E[X] = E[Y] = 4 and var(X)...

Let X and Y be continuous random variables with E[X] = E[Y] = 4 and var(X) = var(Y) = 10. A new random variable is defined as: W = X+2Y+2. a. Find E[W] and var[W] if X and Y are independent. b. Find E[W] and var[W] if E[XY] = 20. c. If we find that E[XY] = E[X]E[Y], what do we know about the relationship between the random variables X and Y?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Let X and Y be jointly normal random variables with parameters E(X) = E(Y ) =...

Let X and Y be jointly normal random variables with parameters E(X) = E(Y ) = 0, Var(X) = Var(Y ) = 1, and Cor(X, Y ) = ρ. For some nonnegative constants a ≥ 0 and b ≥ 0 with a2 + b2 > 0 define W1 = aX + bY and W2 = bX + aY . (a)Show that Cor(W1, W2) ≥ ρ (b)Assume that ρ = 0.1. Are W1 and W2 independent or not? Why? (c)Assume now...

E(Y) = 4, E(X) = E(Y+2), Var(X) = 5, Var(Y) = Var(2X+2) a. What is E(2X...

E(Y) = 4, E(X) = E(Y+2), Var(X) = 5, Var(Y) = Var(2X+2) a. What is E(2X -2Y)? b. What is Var(2X-Y+2)? c. What is SD(3Y-3X)? 2) In a large community, 65% of the residents want to host an autumn community fair. The rest of the residents answer either disagree or no opinion on this proposal. A sample of 18 residents was randomly chosen and asked for their opinions. a) What is th probability that the residents answer either disagree or...

Given: E[x] = 4, E[y] = 6, Var(x) = 2, Var(y) = 1, and cov(x,y) =...

Given: E[x] = 4, E[y] = 6, Var(x) = 2, Var(y) = 1, and cov(x,y) = 0.2 Find a lower bound on (5 < x + y < 10). State the theorem used.

please show all steps Q.4 Let X and Y be continuous random variables with the joint...

please show all steps Q.4 Let X and Y be continuous random variables with the joint pdf: f(x, y) = { k(x + y), if (x, y) ∈ 0 ≤ y ≤ x ≤ 1 ; 0 otherwise Answer the question with the equation below please f(x, y) = 2(x + y), for 0 ≤ y ≤ x ≤ 1 and 0 otherwise. (a) Find E[X + Y ] and E[X − Y ] (b) Find E[XY ] (c) Find...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]

Let X and Y be two continuous random variables with the joint probability density function of...

Let X and Y be two continuous random variables with the joint probability density function of for 0 < x < 2, 0 < y < 2, x + y < 1,where c is a constant. (In all the following answers, you do NOT need to find what the value of c is; just treat it as a number.) (a) Write out the marginal distribution of Y. (b) P(Y < 1/3) = ? (c) P(X < 1.5, Y < 0.5)=...

Question