Question

1. Find the missing value indicated by (A) to make this a valid discrete probability distribution.

x | -10 | 30 | 50 | 90 | 100 |

P(X=x) | 0.05 | 0.10 | 0.25 | 0.15 | A |

2. Calculate the mean of the random variable associated with the
following discrete probability distribution. Do not round your
answer.

x | -1 | 0 | 1 |

P(X=x) | 0.5 | 0.2 | 0.3 |

Answer #1

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

Problem 3. Let x be a discrete random variable with the
probability distribution given in the following table:
x = 50 100 150 200 250 300 350
p(x) = 0.05 0.10 0.25 0.15 0.15 0.20 0.10
(i) Find µ, σ 2 , and σ.
(ii) Construct a probability histogram for p(x).
(iii) What is the probability that x will fall in the interval
[µ − σ, µ + σ]?

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

Determine the required value of the missing probability to make
the distribution a discrete probability distribution.
x
p(x)
3
0.32
4
?
5
0.29
6
0.12

Explain why the following is or is not a valid probability
distribution for the discrete random
variable x.
x
1
0
1
2
3
p(x)
.1
.2
.3
.3
.1

1. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate E(X)
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
2. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate the variance of X
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
3. Given a discrete random variable, X...

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

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

Consider the following random discrete distribution.
x
x(P)
24
0.25
30
0.15
49
0.30
58
0.10
60
0.20
Calculate the mean or the expected value of X
Calculate the variance and the standard deviation of the random
variable

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...

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