You have two 5-sided fair dice. If you roll any individual die, the possible results are...

You have two 5-sided fair dice. If you roll any individual die, the possible results are 1, 2, 3, 4, or 5 each equally likely. Let A1 be the random result on the first die, and A2 be the random result on the second die. We define the random variable A = A1 + A2, the sum of values of two dice. Assume the signal X(t) = A for all times t.

(a) Is A a discrete or a continuous random variable? Why?
(b) What are the possible values that A may take? Make a table.
(c) Find P(A = x), for each possible value of x.
(d) Calculate E(A).
(e) Find Var(A).
(f) Is E[X(t)] independent of t? Explain.
(g) Is Cov(X(t), X(t + τ )) independent of t? Explain.
(h) Is the signal X(t) ergodic? Justify

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Expert Solution

orchestra answered 1 year ago

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