Question

Let X be a continuous random variable uniformly distributed on the interval (0,2). Find E( |X-μ| )

A. 1/12 B. 1/4 C. 1/3 D. 1/2

Answer #1

the continuous random variable X is uniformly distributed over
the interval 4 to 10.What is P(5<=X<=11)?

Let
X be a continuous random variable rv distributed via the pdf f(x)
=4e^(-4x) on the interval [0, infinity].
a) compute the cdf of X
b) compute E(X)
c) compute E(-2X)
d) compute E(X^2)

Suppose that X is a random variable uniformly distributed over
the interval (0, 2), and Y is a random variable uniformly
distributed over the interval (0, 3). Find the probability density
function for X + Y .

A continuous random variable X is uniformly distributed.
The minimum value for X is 20 and the maximum value for X is
120.
Write down the rules for f(x), the density function for
X.
Find the median of this distribution.
Find P(X>40)
Find P( 25 < X < 55)
Find P(X < 75)

3. (10pts) Let Y be a continuous random variable having a gamma
probability distribution with expected value 3/2 and variance 3/4.
If you run an experiment that generates one-hundred values of Y ,
how many of these values would you expect to find in the interval
[1, 5/2]?
4. (10pts) Let Y be a continuous random variable with density
function f(y) = 1 2 e −|y| , −∞ < y < ∞ 0, elsewhere (a) Find
the moment-generating function of...

the
random variable c is uniformly distributed over the integral (5,10)
a) if y=G(x)=4(x^2) , find fy(y)
b) determine E{G(x)}

Let A, B, and C be independent random variables, uniformly
distributed over [0,3], [0,2], and [0,4] respectively. What is the
probability that both roots of the equation Ax2 +Bx+C=0
are real?
The answer is NOT 1/24 nor 7.2981/24 nor .304.

Suppose that X is uniformly distributed on the interval [0,5], Y
is uniformly distributed on the interval [0,5], and Z is uniformly
distributed on the interval [0,5] and that they are
independent.
a)find the expected value of the max(X,Y,Z)
b)what is the expected value of the max of n independent random
variables that are uniformly distributed on [0,5]?
c)find pr[min(X,Y,Z)<3]

Let X represent a continuous random variable with a Uniform
distribution over the interval from 0 to 2. Find the following
probabilities (use 2 decimal places for all answers): (a) P(X ≤
1.92) = (b) P(X < 1.92) = (c) P(0.22 ≤ X ≤ 1.56) = (d) P(X <
0.22 or X > 1.56) =

Let X and Y be independent and identically
distributed random variables with mean μ and variance
σ2. Find the following:
a) E[(X + 2)2]
b) Var(3X + 4)
c) E[(X - Y)2]
d) Cov{(X + Y), (X - Y)}

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