Chapter 8: Q157SE (page 452)

Given that xis a binomial random variable, compute P(x)for each of the following cases:
a. n= 7, x= 3, p= .5
b. n= 4, x= 3, p= .8
c. n= 15, x= 1, p= .1

Short Answer

Expert verified

a. The value of P(x) is 0.2734.

b. The value of P(x) is 0.4096.

c. The value of P(x) is 0.3431.

Step by step solution

Given information

X is a binomial random variable.

Computing the probability distribution p(x) when n = 7, x = 3, p = .5

For a binomial random variable, the probability distribution

$P (x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x}; x = 0, 1, 2, . . ., n$

Here, n = 7 ,x = 3,p = 0.5

$p (x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x} = (\begin{matrix} 7 \\ 3 \end{matrix}) {(0.5)}^{3} {(1 - 0.5)}^{7 - 3} = (\begin{matrix} 7 \\ 3 \end{matrix}) {(0.5)}^{3} {(0.5)}^{4} = 0.2734$

Hence, the probability distributionp(x)is 0.2734.

Computing the probability distribution P(x) when n = 4, x = 3, p = 8

Here n = 4,x = 3, p = 0.8

$p (x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x} = (\begin{matrix} 4 \\ 3 \end{matrix}) {(0.8)}^{3} {(1 - 0.8)}^{4 - 3} = (\begin{matrix} 4 \\ 3 \end{matrix}) {(0.8)}^{3} (0.2) = 4 \times 0.512 \times 0.2 = 0.4096$

Hence, the probability distributionp(x)is 0.4096.

Computing the probability distribution p(x) when n =15, x =1, p = .1

Here,n = 15,x = 1,p=0.1

$p (x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} q^{n - x} = (\begin{matrix} 15 \\ 1 \end{matrix}) {(0.1)}^{1} {(1 - 0.1)}^{15 - 1} = 15 \times 0.1 \times {(0.9)}^{14} = 0.3431$

Hence, the probability distributionp(x)is 0.3431.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Given that xis a binomial random variable, compute P(x)for each of the following cases:
a. n= 7, x= 3, p= .5
b. n= 4, x= 3, p= .8
c. n= 15, x= 1, p= .1

Short Answer

Step by step solution

Given information

Computing the probability distribution p(x) when n = 7, x = 3, p = .5

Computing the probability distribution P(x) when n = 4, x = 3, p = 8

Computing the probability distribution p(x) when n =15, x =1, p = .1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Given that xis a binomial random variable, compute P(x)for each of the following cases:a. n= 7, x= 3, p= .5b. n= 4, x= 3, p= .8c. n= 15, x= 1, p= .1

Short Answer

Step by step solution

Given information

Computing the probability distribution p(x) when n = 7, x = 3, p = .5

Computing the probability distribution P(x) when n = 4, x = 3, p = 8

Computing the probability distribution p(x) when n =15, x =1, p = .1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Logic and Functions

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Given that xis a binomial random variable, compute P(x)for each of the following cases:
a. n= 7, x= 3, p= .5
b. n= 4, x= 3, p= .8
c. n= 15, x= 1, p= .1