1. For the mean and variance of a linear function of a random variable Y = aX + b, where a, b are constants, derive

2. Let X be a real-valued random variable. If E(X) = 1 and var(X) = 5, find

3. *Consider the following data sets:

Estimate the mean and variance of each data set before plotting the data. (Hint: White Gaussian Noise process, the Page 66 of Lecture 5 slides)

1. For the mean and variance of a linear function of a random variable Y = ax +b, where a, b are constants, derive (a) E(Y) =qE(X) + (b) var(Y) = a var( X) 2. Let X be a real-valued random variable. If E(X)= 1 and var(X) = 5, find (a) E[(2 + x)) (b) var(12 +6X) 3. *Consider the following data sets: r(n) ~ WGN(0.1), 1<>