Suppose when a baseball player gets a hit, a single is twice as likely as a double which is twice as likely as a triple which is twice as likely as a home run. Also, the player's batting average, i. e., the probability the player gets a hit, is 0.300. Let B denote the number of bases touched safely during an at-bat. For example, B = 0 when the player makes an out, B = 1 on a single, and so on. What is the PMF of B?

Question

Armani Meyer

Mathematics

3 April, 07:46

Suppose when a baseball player gets a hit, a single is twice as likely as a double which is twice as likely as a triple which is twice as likely as a home run. Also, the player's batting average, i. e., the probability the player gets a hit, is 0.300. Let B denote the number of bases touched safely during an at-bat. For example, B = 0 when the player makes an out, B = 1 on a single, and so on. What is the PMF of B?

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Answers (1)

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Kiera Parrish · Answer 1

The PMF of B is given by

P (B=0) = 0.7

P (B=1) = 0.16

P (B=2) = 0.08

P (B=3) = 0.04

P (B=4) = 0.02

Step-by-step explanation:

Let x denote P (B=1), we know that

P (B=0) = 1-0.3 = 0.7

P (B=1) = x

P (B=2) = x/2

P (B=3) = x/4

P (B=4) = x/8

Also, the probabilities should sum 1, thus

0.7+x+x/2+x/4+x/8 = 1

15x/8 = 0.3

x = 0.16

As a result, the PMF of B is given by

P (B=0) = 0.7

P (B=1) = 0.16

P (B=2) = 0.08

P (B=3) = 0.04

P (B=4) = 0.02