Question

Let X be an Exponential random variable with mean 1. Find the density function for Y = {X}^0.5. Evaluate the density function (to 2 d.p.) of Y at the value 1.4.

Answer #1

TOPIC:Transformation of random variables.

Let X denote a random variable with probability density
function
a. FInd the moment generating function of X
b If Y = 2^x, find the mean E(Y)
c Show that moments E(X ^n) where n=1,4 is given by:

Let X be a continuous random variable with the following
probability density function:
f(x) = e^−(x−1) for x ≥ 1; 0 elsewhere
(i) Find P(0.5 < X < 2).
(ii) Find the value such that random variable X exceeds it 50%
of the time. This value is called the median of the random variable
X.

Let X be a random variable with density function f(x) = 1/4 for
-3 <= x <= 5, and 0 otherwise. Find the density of Y = X^2
and of Y = (X - 1)^2, of Y = |X-1|, and of Y=(X-1)^4.

STAT 180 Let X and Y be independent exponential random variables
with mean equals to 4.
1) What is the covariance between XY and X.
2) Let Z = max ( X, Y). Find the Probability Density Function
(PDF) of Z.
3) Use the answer in part 2 to compute the E(Z).

1 (a) Let f(x) be the probability density function of a
continuous random variable X defined by
f(x) = b(1 - x2), -1 < x < 1,
for some constant b. Determine the value of b.
1 (b) Find the distribution function F(x) of X . Enter the value
of F(0.5) as the answer to this question.

Let Y = X2+X+1
(a) Evaluate the mean and variance of Y, if X is an exponential
random variable.
(b) Evaluate the mean and variance of Y, if X is a Gaussian
random variable.

Let X be a continuous random variable with a probability density function
fX (x) = 2xI (0,1) (x) and let it be the function´
Y (x) = e^−x
a. Find the expression for the probability density function fY (y).
b. Find the domain of the probability density function fY (y).

Let t be a random value of a variable with exponential density e
−t , t > 0, and let Y be Poisson with parameter t. Find P(Y =
2).
A. 1/4
B. 1/2
C. 1/8
D. 1/e

Let X be a random variable with density f X ( x ) = ( 1 / 2 )
cos x for x ∈ [ − π / 2 , π / 2 ]. (a) Show that this is a valid
density function. (b) What is the distribution function of Y = sin
X? (c) What is the density function of Y?

Let X be a random variable with density function f(x) = 2 5 x
for x ∈ [2, 3] and f(x) = 0, otherwise. (a) (6 pts) Compute E[(X −
2)3 ] without attempting to find the density function of Y = (X −
2)3 . (b) (6 pts) Find the density function of Y = (X − 2)3

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 44 seconds ago

asked 18 minutes ago

asked 24 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 42 minutes ago

asked 43 minutes ago

asked 45 minutes ago

asked 51 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago