Suppose X, Y and Z are three different random variables. Let X obey Bernoulli Distribution. The probability distribution function is
p(x) =
Let Y obeys the standard Normal (Gaussian) distribution, which can be written as Y ∼ N(0, 1). X and Y are independent. Meanwhile, let Z = XY .
(a) What is the Expectation (mean value) of X?
(b) Are Y and Z independent? (Just clarify, do not need to prove)
(c) Show that Z is also a standard Normal (Gaussian) distribution, which means Z ∼ N(0, 1)
(d) Are Y and Z uncorrelated(which means Cov(Y, Z) = 0)? (need to prove). (hint: You may need this Theorem about Independence and Functions of Random Variables. Let X and Y be independent random variables. Then, U = g(X) and V = h(Y ) are also independent for any function g and h.)
Please answer all parts.
Thank you!
Homework Answers
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Suppose X, Y and Z are three different random variables. Let X
obey Bernoulli Distribution. The...
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