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The figure shows the probability distribution of a discrete random variable X. Which of the following best describes this random variable?

a. Binomial with n=8,p=0.1

b. Binomial with n=8,p=0.3

c. Binomial with n=8,p=0.8

d. Geometric with p=0.1

e. Geometric with p=0.2

Short Answer

Expert verified

Xis a random variable with a binomial distribution of 8and a probability of0.3.

Step by step solution

01

Given information

According to the graph, the probability distribution is as follows:

X012345678
P(X)0.05
0.20
0.30
0.25
0.150.05
0.01

0.00
0.00
02

Explanation for correct option

The probability distribution given can be written as follows:

P(x=0)=0.05,P(x=1)=0.20P(x=2)=0.25,P(x=3)=0.25P(x=4)=0.15,P(x=5)=0.25P(x=6)=0.01,P(x=7)=0.00122P(x=8)=0.00007

Therefore, the total number of trails is 8, with a success probability of0.3.

Hence, the random variable X has a binomial distribution with a mean of 8 and a probability of 0.3.

As a result, "b" is the correct answer.

03

Explanation for incorrect option

Option A does not describes this random variable of Binomial with n=8,p=0.1

Option C does not describes this random variable of Binomial with n=8,p=0.8

Option D does not describes this random variable of Geometric with p=0.1

Option E does not describes this random variable of Geometric with p=0.2

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Most popular questions from this chapter

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