Answered: In Example 6.14, Y₁ and Y₂ were… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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*6.63 In Example 6.14, Y₁ and Y₂ were independent exponentially distributed random variables, both
with mean B. We defined U₁ = Y₁/(Y₁ + Y₂) and U₂ = Y₁+ Y₂ and determined the joint
density of (U₁, U₂) to be
0₁.0₂(₁,₂)=242€¯
0,
0<u₁ <1, 0< u₂,
otherwise.
Show that U₁ is uniformly distributed over the interval (0, 1).
a
b
Show that U₂ has a gamma density with parameters α = 2 and B.
c Establish that U₁ and U₂ are independent.

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