Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:...

Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:

?_x(1)= 1/2 ?_x(2)= 1/2 ?_Y(3)= 1/3 ?_Y(4)= 2/3

(a) Write down the joint PMF

(b) Calculate ?(? + ? ≤ 5) and ? (? − ? ≥ 2)

(c) Calculate ?(?? ), ?(?²? ),Calculate E((X²+1)/(Y-2))

(d) Calculate the C??(?, ? ), C??(1 − ?, 3? + 2) and V??(2? − ? )

(e) Calculate C??(??, ?), C??(??, ? + ? ) and V?? (?/Y)

Expert Solution

orchestra answered 2 years ago

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Let ? ∈ {1, 2} and ? ∈ {3, 4} be independent random variables with PMF-s:...

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