(1) A continuous random variable W has p.d.f f(w) = 2w, for 0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 42CR
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(1)
A continuous random variable W has p.d.f
for 0 <w< 1
{
Given W = w, a random variable T has conditional p.d.f
0<t< w;
f(w) =
f(t|w) =
2w,
0, otherwise.
W
0,
(a) Find the joint p.d.f of W and T, f(w,t).
(b) Find the marginal p.d.f. of T.
otherwise
(c) Find the mean of T, μT.
(d) Find the variance of T, o7.
(e) Given T = t, find the conditional p.d.f. of W, f(w|t).
(f) Find E[W\t], for 0 <t < 1.
(g) Find o₁, for 0 <t<1.
Transcribed Image Text:(1) A continuous random variable W has p.d.f for 0 <w< 1 { Given W = w, a random variable T has conditional p.d.f 0<t< w; f(w) = f(t|w) = 2w, 0, otherwise. W 0, (a) Find the joint p.d.f of W and T, f(w,t). (b) Find the marginal p.d.f. of T. otherwise (c) Find the mean of T, μT. (d) Find the variance of T, o7. (e) Given T = t, find the conditional p.d.f. of W, f(w|t). (f) Find E[W\t], for 0 <t < 1. (g) Find o₁, for 0 <t<1.
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