Question

The random variables *X* and *Y* are independent.
*X* has a Uniform distribution on [0, 5], while *Y*
has an Exponential distribution with parameter λ = 2. Define *W
= X + Y*.

A. What is the expected value of
*W*?

B. What is the standard deviation of
*W*?

C. Determine the pdf of
*W*. *For full credit, you need to write out
the integral(s) with the correct limits of integration. Do not
bother to calculate the integrals.*

Answer #1

X and Y are independent variables, with X having a uniform (0,1)
distribution and Y being an exponential random variable with a mean
of 1.
Given this information, find P(max{X,Y} > 1/2)

If X ~ Binomial (n, p) and Y ~ Binomial (m, p) are independent
variables with the same probability p, what is the distribution for
Z=X+Y? Is it still a binomial distribution? Write out the pdf for Z
if it is binomial, otherwise, explain why it is not. What about W =
X-Y, is it a binomial distribution? Write out the pdf for W if it
is binomial, otherwise, explain why it is not.

Let U1 and U2 be independent Uniform(0, 1) random variables and
let Y = U1U2.
(a) Write down the joint pdf of U1 and U2.
(b) Find the cdf of Y by obtaining an expression for FY (y) =
P(Y ≤ y) = P(U1U2 ≤ y) for all y.
(c) Find the pdf of Y by taking the derivative of FY (y) with
respect to y
(d) Let X = U2 and find the joint pdf of the rv pair...

Let X and Y be independent random variables, with X following
uniform distribution in the interval (0, 1) and Y has an Exp (1)
distribution.
a) Determine the joint distribution of Z = X + Y and Y.
b) Determine the marginal distribution of Z.
c) Can we say that Z and Y are independent? Good

Assume that X and Y are independent random variables, each
having an
exponential density with parameter λ. Let Z = |X - Y|. What is the
density of Z?

Let X denote a random variable that follows a binomial
distribution with parameters n=5, p=0.3, and Y denote a random
variable that has a Poisson distribution with parameter λ = 6.
Additionally, assume that X and Y are independent random
variables.
Using the joint pdf function of X and Y, set up the summation
/integration (whichever is relevant) that gives the expected value
for X, and COMPUTE its value.

Let X denote a random variable that follows a binomial
distribution with parameters n=5, p=0.3, and Y denote a random
variable that has a Poisson distribution with parameter λ = 6.
Additionally, assume that X and Y are independent random
variables.
Using the joint pdf function of X and Y, set up the summation
/integration (whichever is relevant) that gives the expected value
for X, and COMPUTE its value.

Suppose that X and Y are independent Uniform(0,1) random
variables. And let U = X + Y and V = Y .
(a) Find the joint PDF of U and V
(b) Find the marginal PDF of U.

Let X and Y be independent random variables each having the
uniform distribution on [0, 1].
(1)Find the conditional densities of X and Y given that X > Y
.
(2)Find E(X|X>Y) and E(Y|X>Y) .

Let X and Y be independent random variables following Poisson
distributions, each with parameter λ = 1. Show that the
distribution of Z = X + Y is Poisson with parameter λ = 2. using
convolution formula

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 48 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago