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the last bit of the solution is incorrect as this is not a standard exp r.v.

the last bit of the solution is incorrect as this is not a standard exp r.v.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.10: Partial Fractions
Problem 21E
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the last bit of the solution is incorrect as this is not a standard exp r.v.

∞ = _ x*fx/x+y(x/x+y) dx -∞ E(XIX+Y)= = 5_²_x ₁ ( {x,x+ x(x₁x + y)) -∞ fx+y(x+y) a³-(x+y).e-a(2x+y) a² (x+y) e -a(2x+y) a.e -a(x+y) = 50 = X = √³x² X. -∞ = = 500 x. (a.e-ax) dx -∞ = a S e = 50 × x-(a-e-2ax-ay+ax + ay) dx -∞ 88 x.e dx -ax dx -a(x+y) 2)dx dx incorrect This is a standard exponential random variable with parameter a, so the expected value is a The conditional expectation of E(X|X+Y) is 1/1 a
Transcribed Image Text:∞ = _ x*fx/x+y(x/x+y) dx -∞ E(XIX+Y)= = 5_²_x ₁ ( {x,x+ x(x₁x + y)) -∞ fx+y(x+y) a³-(x+y).e-a(2x+y) a² (x+y) e -a(2x+y) a.e -a(x+y) = 50 = X = √³x² X. -∞ = = 500 x. (a.e-ax) dx -∞ = a S e = 50 × x-(a-e-2ax-ay+ax + ay) dx -∞ 88 x.e dx -ax dx -a(x+y) 2)dx dx incorrect This is a standard exponential random variable with parameter a, so the expected value is a The conditional expectation of E(X|X+Y) is 1/1 a
Definitions [edit] Probability density function [edit] The probability density function (pdf) of an exponential distribution is de-Ax f (x; X) = { 0 Here >> 0 is the parameter of the distribution, often called the rate parameter. The distribution is supported on the interval [0, ∞). If a random variable X has this distribution, we write X~ Exp(2). The exponential distribution exhibits infinite divisibility. F(x; λ) x ≥ 0, x < 0. Cumulative distribution function [edit] The cumulative distribution function is given by = (1 -xx e 0 x > 0, x < 0.
Transcribed Image Text:Definitions [edit] Probability density function [edit] The probability density function (pdf) of an exponential distribution is de-Ax f (x; X) = { 0 Here >> 0 is the parameter of the distribution, often called the rate parameter. The distribution is supported on the interval [0, ∞). If a random variable X has this distribution, we write X~ Exp(2). The exponential distribution exhibits infinite divisibility. F(x; λ) x ≥ 0, x < 0. Cumulative distribution function [edit] The cumulative distribution function is given by = (1 -xx e 0 x > 0, x < 0.
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