Concept explainers
a.
Find the joint probability distribution of
a.
Answer to Problem 68E
The joint probability distribution of
Explanation of Solution
Calculation:
Consider that
The two discrete random variables
Binomial distribution:
A random variable Y is said to follows binomial distribution if and only if the probability mass function is defined as,
According to the question
Hence, according to the given question the probability mass function of
Similarly, according to the given question the probability mass function of
As
That is,
As these two random variables are independent then the joint probability distribution would be the product of the marginal distributions.
That is,
Thus, the joint probability distribution of
b.
Find the probability that not more than one of the three customers will spend more than $50.
b.
Answer to Problem 68E
The probability that not more than one of the three customers will spend more than $50 is 0.864.
Explanation of Solution
Calculation:
The probability that not more than one of the three customers will spend more than $50 can be written as
Hence, using the joint probability function the required probability is obtained as,
The value of
The value of
The value of
Thus,
Thus, the probability that not more than one of the three customers will spend more than $50 is 0.864.
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Chapter 5 Solutions
Mathematical Statistics with Applications
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