Answered: 5.85 In Exercise 5.65, we considered… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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5.85 In Exercise 5.65, we considered random variables Y1 and Y2 that, for –1 < a < l, have joint
density function given by
[1 – a{(1 – 2e-yı)(1 – 2e¬9½)}]e-yi¬y2, 0<yı,0 < y2,
f (y1, y2) =
0,
elsewhere
and established that the marginal distributions of Y1 and Y, are both exponential with mean 1.
Find
a E(Y1) and E(Y2).
b V(Y) and V (Y2).
c (Y1 – Y2).
d E(Y¡Y2).
e
V (Y – Y2). Within what limits would you expect Y, – Y2 to fall?

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