What is the correlation and covariance of a function of random variables?

mangicele4s 2022-09-23 Answered
If I have that X and Y are independent r.v with mean 0 and variance σ 2 and I have that
Z = X sin α + Y cos α , what is then the covariance and the correlation between X and Z?
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Answers (1)

ahem37
Answered 2022-09-24 Author has 15 answers
Step 1
You have :
c o v ( X , Z ) = E [ X ( X sin α + Y cos α ) ] = sin α × E ( X 2 ) + cos α × E ( X Y ) = σ 2 sin α + cos α × c o v ( X , Y ) = σ 2 sin α  (because  X  and  Y  are independant)
And you can also get the correlation :
R = sin α
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