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Exercises
1- Determine the probability distribution’s missing
The random variable x represent the number of the dependent children in
the households.
X
0
1
2
3
4
p(x)
0.07
0.20
0.38
?
0.13
In exercise 2-3 Decide whether the distribution is a probability distribution .if
it is not a probability distribution, identify the property (or properties) that are
not satisfied
2- The random variable x represents the possible test scores
X
0
1
2
3
4
P(x)
0.05
0.25
0.35
0.25
0.10
3- The random variable x represent the number of imperfections found
X
0
1
2
3
4
5
3
1
1
1
1
−1
P(x)
4
10
20
25
50
100
4- Students in a class take a quiz with 8 questions. The number x of questions
answered correctly can be approximated by the following probability
distribution.
Find
a) Mean ,b)variance ,c) standard deviation
X
0
1
2
3
4
5
6
7
8
P(x)
0.02
0.02
0.06
0.06
0.08
0.22
0.30
0.16
0.08
5-The random variable X has the following function 𝑃(𝑥)
a.
b.
c.
d.
e.
x
4
5
6
7
P( X  x)
1
16
1
16
1
4
3
16
8
9
1
8
5
16
 Prove that P(x) is probability mass function.
Find the expected value ofX.
Find the variance and standard deviation.
Find the cumulative distribution𝐹(𝑋).
Find 𝑃(𝑋 > 3), 𝑃(4 < 𝑋 < 7), 𝑃(𝑋 = 6.5) .
2
Find 𝐸(2𝑋), 𝜎2𝑋
6- The following table is the probability distribution function of a discrete
random variable X .
a.
b.
c.
d.
e.
f.
X
0
1
3
4
6
P( X  x)
k
0.3
0.3
0.2
0.1
Find the value of k.
Find the expected value of 𝑋 (𝐸(𝑋)).
Find the cumulative distribution𝐹(𝑋).
Find the variance and standard deviation.
Find (𝑋 ≥ 4), 𝑃(1 ≤ 𝑋 ≤ 4), 𝑃(𝑋 = −1) .
2
Find 𝐸(𝑋 + 1), 𝜎𝑋+1