Concept explainers
a.
Find the joint
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.
Want to see more full solutions like this?
Chapter 5 Solutions
Mathematical Statistics with Applications
- A manufacturer has determined that a machine averages one faulty unit for every 500 it produces. What is the probability that an order of 300 units will have one or more faulty units?arrow_forwardShow that the probability of drawing a club at random from a standard deck of 52 playing cards is the same as the probability of drawing the ace of hearts at random from a set of four cards consisting of the aces of hearts, diamonds, clubs, and spades.arrow_forwardIf a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage