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

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
parameter λ and that λ|p is geometric with parameter p. Further
suppose that p is uniform between zero and one. Determine the pdf
for the random variable X and compute E(X).

X and Y are independent. X is Rayleigh random variable with a
parameter 5 and y is exponential with a parameter of 5. Obtain the
mean of and variance of Z=4X+6Y

Let X be a Poisson random variable with parameter λ and Y an
independent Bernoulli random variable with parameter p. Find the
probability mass function of X + Y .

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
larger than Y, i.e., find P(X>Y). [Hint: Unlike Problem 1b, we
do not have symmetry between X and Y here, so you must
calculate.]

Let X be a geometric random variable with parameter p . Find the
probability that X≥10 . Express your answer in terms of p using
standard notation (click on the “STANDARD NOTATION" button
below.)

The random variable W = X – 3Y + Z + 2 where X, Y and Z are
three independent Normal random variables, with E[X]=E[Y]=E[Z]=2
and Var[X]=9,Var[Y]=1,Var[Z]=3.
The pdf of W is:
Uniform
Poisson
Binomial
Normal
None of the other pdfs.

Let X and Y be independent Geometric(p) random variables. What
is P(X<Y)?

If
? and ? are both identical but independent Geometric random
variables with parameter ?, find the probability that ?(? = ?).

(14pts) Let X and Y be i.i.d. geometric random variables with
parameter (probability of success) p, 0 < p < 1. (a) (6pts)
Find P(X > Y ). (b) (8pts) Find P(X + Y = n) and P(X = k∣X + Y =
n), for n = 2, 3, ..., and k = 1, 2, ..., n − 1.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 9 minutes ago

asked 17 minutes ago

asked 21 minutes ago

asked 38 minutes ago

asked 38 minutes ago

asked 45 minutes ago

asked 46 minutes ago

asked 53 minutes ago