   # Kittens Use the frequency distribution in Exercise 6 to find the probability distribution for the random variable. Kittens A cat has a litter of four kittens. Let x represent the number of male kittens. x 0 1 2 3 4 n ( x ) ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 8RE
Textbook Problem
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## Kittens Use the frequency distribution in Exercise 6 to find the probability distribution for the random variable.Kittens A cat has a litter of four kittens. Let x represent the number of male kittens. x 0 1 2 3 4 n(x)

To determine

To calculate: The probability distribution of the random variable x which is defined as the number of male kittens in a litter of four kittens using the frequency distribution.

### Explanation of Solution

Given Information:

A cat has a litter of four kittens. The random variable x is defined as the number of male kittens.

Formula used:

The probability of a random variable x is defined as,

P(x)=n(x)n(S)

Here, n(x) is the frequency of x and n(S) is the number of outcomes in S.

Calculation:

Consider that a cat has a litter of four kittens.

Define the random variable x as the number of male kittens.

For a kitten with litter of four kittens, there will be 16 possible combinations of males and females. So, the sample space is:

S={MMMM,FMMM,MFMM,MMFM,MMMF,FFMM,FMFM,FMMF,MFFM,MFMF,MMFF,MFFF,FMFF,FFMF,FFFM,FFFF}

As the random variable x is defined as the number of male kittens in the litter, the possible values of number of occurrence of male kittens in all the outcomes are 0,1,2,3,4. To find the frequencies, count the number of occurrence of male kittens in all the outcomes in the sample space.

For x=0, that is no male kitten in the litter, the number of outcomes without males is one.

For x=1, the number of outcomes with one male kitten is four.

For x=2, the number of outcomes with two male kittens is six.

For x=3, the number of outcomes with three male kittens is four.

For x=4, the number of outcomes with four male kittens is one

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