(a) To determine To calculate: The value of p ( X ) , X = 0 , 1 , 2 , 3 , using the formula for a binomial probability distribution. Explanation Given info: The random variable X is a binomial random variable and the probability distribution is given by, p ( x ) = ( n x ) ( p ) x ( 1 − p ) n − x , Where, n is number of trials, x is number of successes among n trials, p is probability of success, q is probability of failure and n − x is the number of failures in n trials. Calculation: Substitute, n = 3 and p = 0.3 The probability distribution for X = 0 can be obtained as follows: p ( x = 0 ) = ( 3 x ) ( 0.3 ) x ( 1 − 0.3 ) 3 − x = ( 3 0 ) ( 0.3 ) 0 ( 1 − 0.3 ) 3 − 0 = 3 ! 0 ! 3 ! ( 0.3 ) 0 ( 0.7 ) 3 = 3 × 2 × 1 1 × 3 × 2 × 1 ( 1 ) ( 0.7 ) 3 = 0.343 Thus, the required probability is, p ( 0 ) = 0.343 _ The probability distribution for X = 1 can be obtained as follows: p ( 1 ) = ( 3 x ) ( 0.3 ) x ( 1 − 0.3 ) 3 − x = ( 3 1 ) ( 0.3 ) 1 ( 1 − 0 (b) To determine To find: The probability distribution for X in tabular form, using the answer to part a.

13th Edition

ISBN: 9780135819999

Author: MCCLAVE

Publisher: PEARSON CO

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Chapter 4.4, Problem 62LM

(a)

To determine

To calculate: The value of p(X) , X=0, 1, 2, 3, using the formula for a binomial probability distribution.

(b)

To determine

To find: The probability distribution for X in tabular form, using the answer to part a.

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Chapter 4.4, Problem 61LM

Chapter 4.4, Problem 63LM

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