Explanation Calculation : It is given that Γ ( 1 2 ) = ∫ 0 ∞ y − 1 2 e − y d y . Hence, Γ ( 1 2 ) = ∫ 0 ∞ y − 1 2 e − y d y = ∫ 0 ∞ ( x 2 2 ) − 1 2 e − x 2 2 x d x { ∵ y = x 2 2 , d y = x d x } = 2<

Mathematical Statistics with Applications

7th Edition

ISBN: 9781111798789

Author: Dennis O. Wackerly

Publisher: Cengage Learning

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Chapter 4, Problem 196SE

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Prove that Γ(12)=π.

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Chapter 4, Problem 195SE

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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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Prove that Γ ( 1 2 ) = π .

Solution Summary: The author calculates that BeginarraycGamma(12)=displaystyle.

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