I am not sure how to complete this problem please explain your process and reaso

Question

I am not sure how to complete this problem please explain your process and reasoning.
I also am having trouble calculating equation on a calculator, so if you use a specific function on it to calculate it please state what you used so that I can learn what it is.

:) Thank you.

1. A random vector (X, Y ) has a probability mass function with the following characteristics:

µX = 5, 2 X = 25, µY = 10, Y = 36, = .80

(a) What is the best linear predictor of Y given X = x?

(b) If you are told that the value of X is 15, what is your prediction of Y based on the best linear predictor in

Remark: Recall in the lecture during March 8 that the best linear predictor of Y given X = x is L(x) = µY + (x µX) where = Y /X.

Explanation / Answer

a)(Note:here please revert if for above 2y is not 36 as it is given without square sign)

here slope b1 =*y/x =0.8*(36/25)1/2=0.96

and intercept =µY-b1*µX =10-0.96*5=5.2

hence  best linear predictor of Y given X = x =µY|X=x =5.2+0.96x

b) prediction of Y =5.2+0.96*15=19.6

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