Q.97 In major league baseball, a no-h... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 5: Q.97 (page 357)

In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential.
a. What is the probability that an entire season elapses with a single no-hitter?
b. If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season?
c. What is the probability that there are more than $3$ no-hitters in a single season?

Short Answer

Expert verified

a). The probability that an entire season elapses with a single no-hitter is $0.0498$ .

b). The value of $P (T > 2 鈭� T > 1)$ is $0.0498$ .

c). The value of $P (x > 3)$ is $0.3528$ .

Step by step solution

Part (a) Step 1: Given Information

$X ~ Exp (3)$

Where.

$m = 3$

$渭 = \frac{1}{3}$

$= 0.3333$

Part (a) Step 2: Explanation

The required probability can be calculated as below:

$P (x > 1) = 1 - P (x < 1)$

$= 1 - (1 - e^{- 3 - 1})$

= e^{- 3}

$= 0.0498$

Part (b) Step 1: Given Information

$X ~ Exp (3)$

Where.

$m = 3$

$渭 = \frac{1}{3}$

$= 0.3333$

Part (b) Step 2: Explanation

The required probability can be written as $P (T > 2 鈭� T > 1)$ . Now, use the memory less property of exponential distribution. That is,

$P (x > t + r 鈭� x > t) = P (x > r)$

So,

$P (T > 2 鈭� T > 1) = P (T > 1 + 1 鈭� T > 1)$

$= P (T > 1)$

$= 0.0498$

Therefore, the value of $P (T > 2 鈭� T > 1)$ is $0.0498$ .

Part (c) Step 1: Given Information

$X ~ Exp (3)$

Where.

$m = 3$

$渭 = \frac{1}{3}$

$= 0.3333$

Part (c) Step 2: Explanation (Part c)

Let $X =$ the number of no-hitters is a season. Assume that $X$ is Poisson with mean $位 = 3$ . Then,

localid="1650470480426" $P (X > 3) = 1 - P (X 鈮� 3) = 0.3528$ .

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Part (c) Step 1: Given Information

Part (c) Step 2: Explanation (Part c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Calculus

Decision Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.