Question

Let X be a discrete random variable that takes on the values −1, 0, and 1. If E (X) = 1/2 and Var(X) = 7/16, what is the probability mass function of X?

Answer #1

Q6/
Let X be a discrete random variable defined by the
following probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Give P(4≤ X < 8)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q7/
Let X be a discrete random variable defined by the following
probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Let F(x) be the CDF of X. Give F(7.5)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q8/
Let X be a discrete random variable defined by the following
probability function :
x
2
6...

Let X be a discrete random variable with probability mass
function (pmf) P (X = k) = C *ln(k) for k = e; e^2 ; e^3 ; e^4 ,
and C > 0 is a constant.
(a) Find C.
(b) Find E(ln X).
(c) Find Var(ln X).

A Poisson random variable is a variable X that takes on the
integer values 0 , 1 , 2 , … with a probability mass function given
by p ( i ) = P { X = i } = e − λ λ i i ! for i = 0 , 1 , 2 … ,
where the parameter λ > 0 .
A)Show that ∑ i p ( i ) = 1.
B) Show that the Poisson random...

The range of a discrete random variable X is {−1, 0, 1}. Let MX
(t) be the moment generating function of X, and let MX(1) = MX(2) =
0.5. Find the third moment of X, E(X^3).

The range of a discrete random variable X is {−1, 0, 1}. Let
MX(t) be the moment generating function of X, and let MX(1) = MX(2)
= 0.5. Find the third moment of X, E(X^3 )

Suppose X is a discrete random variable that takes on integer
values between 1 and 10, with variance Var(X) = 6. Suppose that you
define a new random variable Y by observing the output of X and
adding 3 to that number. What is the variance of Y? Suppose then
you define a new random variable Z by observing the output of X and
multiplying that by -4. What is the variance of Z?

Let X be a discrete random variable with values 1,2,3,4,5 and
corresponding proba- bilities 1/7, 1/14, 3/14, 2/7, 2/7. a) Compute
E(X) b) compute E[|X − 2|].

Let x be a discrete random variable with the following
probability distribution
x: -1 , 0 , 1, 2
P(x) 0.3 , 0.2 , 0.15 , 0.35
Find the mean and the standard deviation of x

Suppose X is a discrete random variable with probability mass
function given by
p (1) = P (X = 1) = 0.2
p (2) = P (X = 2) = 0.1
p (3) = P (X = 3) = 0.4
p (4) = P (X = 4) = 0.3
a. Find E(X^2) .
b. Find Var (X).
c. Find E (cos (piX)).
d. Find E ((-1)^X)
e. Find Var ((-1)^X)

Let X be a random variable with probability density function
fX(x) = {c(1−x^2)if −1< x <1, 0 otherwise}.
a) What is the value of c?
b) What is the cumulative distribution function of X?
c) Compute E(X) and Var(X).

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