Question

If X and Y are independent, where X is a geometric random variable with parameter 3/4 and Y is a standard normal random variable. Compute E(e X), E(e Y ) and E(e X+Y ).

Answer #1

We have to calculate E(eX),E(eY),E(eX+Y)

Where X and Y are independent

And. X~geometric(3/4)

AndY~N(0,1)

If X and Y are independent, where X is a geometric random
variable with parameter 3/4 and Y is a standard normal random
variable. Compute E(e^X), E(e^Y ) and E(e^(X+Y) ).

Suppose that X|λ is an exponential random variable with
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Let X be a Poisson random variable with parameter λ and Y an
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Suppose X and Y are independent Geometric random variables, with
E(X)=4 and E(Y)=3/2.
a. Find the probability that X and Y are equal,
i.e., find P(X=Y).
b. Find the probability that X is strictly
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Poisson
Binomial
Normal
None of the other pdfs.

Let X and Y be independent Geometric(p) random variables. What
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? and ? are both identical but independent Geometric random
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Find P(X > Y ). (b) (8pts) Find P(X + Y = n) and P(X = k∣X + Y =
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