a. Explanation The random variable Y is a beta distribution with α = 4 and β = 7 . The relation between the distribution function of a beta-distributed random variables and sums of binomial probabilities is given below: F ( Y ) = ∫ 0 y t α − 1 ( 1 − t ) β − 1 B ( α , β ) d t = ∑ i = α n ( n i ) y i ( 1 − y ) n − i Where, n = α + β − 1 Here, n = α + β − 1 = 4 + 7 − 1 = 10 The probability of Y less than or equal to 0 b. To determine Find P ( Y ≤ 0.6 ) = F ( 0.6 ) , if Y has a beta distribution with α = 12 and β = 14 . c. To determine Use the applet Beta probabilities and Quantiles to find the probabilities in Parts ‘ a’ and ' b’ .

Mathematical Statistics with Applications

7th Edition

ISBN: 9781111798789

Author: Dennis O. Wackerly

Publisher: Cengage Learning

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Chapter 4.7, Problem 134E

To determine

Find P(Y≤0.7)=F(0.7), if Y has a beta distribution with α=4 and β=7.

To determine

Find P(Y≤0.6)=F(0.6), if Y has a beta distribution with α=12 and β=14.

To determine

Use the applet Beta probabilities and Quantiles to find the probabilities in Parts ‘a’ and 'b’.

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Chapter 4.7, Problem 133E

Chapter 4.7, Problem 135E

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Chapter 4 Solutions

Mathematical Statistics with Applications

Ch. 4.2 - Prob. 1E Ch. 4.2 - A box contains five keys, only one of which will...Ch. 4.2 - A Bernoulli random variable is one that assumes...Ch. 4.2 - Let Y be a binomial random variable with n = 1 and...Ch. 4.2 - Suppose that Y is a random variable that takes on...Ch. 4.2 - Consider a random variable with a geometric...Ch. 4.2 - Let Y be a binomial random variable with n=10 and...Ch. 4.2 - Prob. 8E Ch. 4.2 - A random variable Y has the following distribution...Ch. 4.2 - Refer to the density function given in Exercise...

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Find P ( Y ≤ 0.7 ) = F ( 0.7 ) , if Y has a beta distribution with α = 4 and β = 7 .

Solution Summary: The author explains the relation between the distribution function of a beta-distributed random variables and sums of binomial probabilities.

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Find P(Y≤0.7)=F(0.7), if Y has a beta distribution with α=4 and β=7.

Find P(Y≤0.6)=F(0.6), if Y has a beta distribution with α=12 and β=14.

Use the applet Beta probabilities and Quantiles to find the probabilities in Parts ‘a’ and 'b’.

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Chapter 4 Solutions