(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is?

Answer is 1/2

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Request

2. Relevant equations

the expectation value of any function g is, <g>=∫Ψ*gΨdx

3. The attempt at a solution

Here,

Ψ=f(x)

since f is independent of time

∴Ψ*=f(x)

now, for <cos 4x>=∫exp(-4x)cos(4x)exp(-4x)dx

let <cos4x>=I=∫cos(4x)exp(-8x)dx

rest of the solution if in the picture attached

my main doubt is how to put the limit infinity in sin and cos

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# Homework Help: how to find the expectation value of cos x

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