Fact: If X is a compound random variable with X = ₁X₁, ther E(X) = E(X₁) E(N) a. when X are all discrete b. when X are all continuous

Q: Prove - If X and Y are independent random variables, then E(XY ) = E(X)E(Y ). (You can assume that…

A: Assume that X and Y are two independent discrete random variables.

Q: Calculate E((X +Y)²).

A:

Q: 5. If X is an exponential random variable with parameter 2, and c > 0, show cX is exponential with…

A: Using transformation of cumulative distribution

Q: E(Y) –> P(Y > n).

A:

Q: 3. If X and Y are independent uniform (0, 1) random variables, show that 2 for a > 0 (a + 1)(a + 2)…

A: X and Y are independent U(0,1) random variables:Objective: Show that:

Q: 4. Let X be a random variable taking positive values and assume that E(X) exists. Which of the…

A: Option (I) is correct as E(X2)>= (E(X))2 when we find Variance.

Q: ). If X is a continuous random variable whose pdf is f(x): (a) 0 (b) 1 (c) 1/4 (d) 4 (e) None of the…

A: 0 \)" data-mce-style="cursor: default;">f(x)=c(1+x)4;x>0

Q: uppose X and Y are independent random variables. If the pdf of x is xe ",x ≥ 0 and the pdf of y is…

A: Solution

Q: (1) E(E(X)) = E(X) (2) E(X – E(X)) = 0 (3) Var(X) = E(X²) – [E(X)]² (4) Given constants a and b,…

A: Discrete random variable is defined as a variable which can take only specific values. For example…

Q: 13. The loss random variable X has a probability generating function 1 P(z) = = 2-z What is E[XA 3]?

A:

Q: 6. Suppose X is a random variable with E(X) = 4 and Var(X) = 9. Let Y = 4X + 5. Compute E(Y) and…

A: In question, Given E(X) = 4 and Var(X)=9 Y=4X+5 Then we'll find the value of E(Y). The solution is…

Q: 3. Let X and Y be two independent Bernoulli (0.5) random variables. Let Z = X + Y. Show that Var (Z)…

A: Bernoulli Distribution: You should understand what a Bernoulli random variable is and know its…

Q: 1. Let X1, X2, X3 be identically distributed independent exponential random variables and Y = X₁+ X2…

A: Given that X​1, X2​, and X3​ are identically distributed independent exponential random variables…

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

Q: If the probability den sity function of a continu ous random variable X is [a+ ba² 0<x <1 f(x) :…

A: