Question

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)

Answer #1

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) .

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.

X and Y are independent and identically distributed variables
uniform over [0,1]. Find PDF of A=Y/X

Assume X and. Y are. 2. independent variables that follow the
standard uniform distribution i.e. U(0,1)
Let Z = X + Y
Find the PDF of Z, fZ(z) by first obtaining the CDF
FZ(z) using the following steps:
(a) Draw an x-y axis plot, and sketch on this plot the lines
z=0.5, z=1, and z=1.5 (remembering z=x+y)
(b) Use this plot to obtain the function which describes the
area below the lines for z = x + y in terms...

Let X and Y be independent exponential random variables with
respective rates ? and ? Is max(X, Y ) an exponential random
variable?

Let X and Y be independent and identical uniform distribution on
[0,1]. Let Z=min(X, Y). Find E[Y-Z]. What is the probability
Y=Z?

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.

Let X be continuous uniform (0,1) and Y be exponential (1). Let
O1 = min(X,Y) and O2 = max(X,Y) be the order statistics of ,Y. Find
the joint density of O1, O2.

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

(a) Given two independent uniform random variables X, Y in the
interval (−1, 1), find E |X − Y |.
(b) Let X, Y be as in (a). Find the support and density of the
random variable Z = |X − Y |.
(c) From (b), compute the mean of Z and check whether you get
the same answer as in (a)

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