Question

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)

Answer #1

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).

Question 1
Refer to the probability function given in the following table
for a
random variable X that takes on the values 1,2,3 and 4
X 1 2 3 4
P(X=x) 0.4 0.3 0.2 0.1
a) Verify that the above table meet the conditions
for being a discrete probability
distribution
b) Find P(X<2)
c) Find P(X=1 and X=2)
d) Graph P(X=x)
e) Calculate the mean of the random variable
X
f) Calculate the standard deviation of the random
variable X...

Consider a discrete random variable X with probability mass
function P(X = x) = p(x) = C/3^x, x = 2, 3, 4, . . . a. Find the
value of C. b. Find the moment generating function MX(t). c. Use
your answer from a. to find the mean E[X]. d. If Y = 3X + 5, find
the moment generating function MY (t).

1. Let X be a discrete random variable with the probability mass
function P(x) = kx2 for x = 2, 3, 4, 6.
(a) Find the appropriate value of k.
(b) Find P(3), F(3), P(4.2), and F(4.2).
(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).
(d) Find the mean µ and the variance σ 2 of X. [Note: For a
random variable, by definition its mean is the same as its
expectation, µ = E(X).]

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...

given the discrete probability distribution below:
x
10
20
30
40
50
P(x)
0.3
0.05
0.1
0.05
0.2
calculate:
a. E(x)
b. Var(x)
c. σx

Determine whether or not the table is a valid probability
distribution of a discrete random variable. Explain fully.
a.
x
-2
0
2
4
P(x)
0.3
0.5
0.2
0.1
b.
x
0.5
0.25
0.25
P(x)
-0.4
0.6
0.8
c.
x
1.1
2.5
4.1
4.6
5.3
P(x)
0.16
0.14
0.11
0.27
0.22

The following table denotes the probability distribution for a
discrete random variable X.
x
-2
0
1
2
9
p(x)
0.1
0.3
0.2
0.3
0.1
The standard deviation of X is closest to
Group of answer choices
3.74
4.18
2.77
7.65
11

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

If X is a random variable with a probability distribution that
is given in the following table where a and b are unknown
constants.
X -1 0 a 3 b P(X = x) 0.1 0.15a 0.2 0.03b 0.4
(a) Find a and b such that E(5 + 100X) = 260.
(b) Find the variance of X.

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