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After scoring a touchdown, a football team may elect to

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 1E Chapter 4.1

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 1E

After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.

a. Let X = 1 if successful, X = 0 if not. Find the mean and variance of X.

b. If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.

c. Find the mean and variance of Y.

Step-by-Step Solution:

Answer:

Step 1 of 3:

(a)

In this question, we are asked to find the mean and variance of .

Where  is random variable of team scoring successfully two points in the football game.

For a certain football team, the probability that this play is successful is .

Let if successful, if not.

If the random event results in success, then . Otherwise . It follows that  is a discrete random variable, with probability mass function (PMF) defined by

       

             

 for any value of x other than 0 or 1

The random variable  is said to have the Bernoulli distribution with parameter .

And the notation is  ∼ Bernoulli().

Mean) of a Bernoulli random variable

 ………….(1)

Where  is probability of success of any event which is given in the question.

Substitute the value of into the equation (1)

Variance  of a Bernoulli random variable

 ………….(2)

Substitute the value of into the equation (2)

Hence mean and variance of  is and respectively.


Step 2 of 3

Chapter 4.1, Problem 1E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.a. Let X = 1 if successful, X = 0 if not. Find the mean and variance of X.________________b. If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.________________c. Find the mean and variance of Y.” is broken down into a number of easy to follow steps, and 112 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 1E from chapter: 4.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: team, successful, points, Find, scores. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 1E from 4.1 chapter was answered, more than 1612 students have viewed the full step-by-step answer.

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