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

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Basic Math

Let ? ? {1, 2} and ? ? {3, 4} be independent random variableswith PMF-s: ??(1)= 1/2 ??(2)= 1/2 ??(3)= 1/3 ??(4)= 2/3

Answer the following questions

(a) Write down the joint PMF

(b) Calculate?(?+??5)and?(? ???2) 2 ?2+1

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

(?*) Calculate C??(??, ?), C??(??, ? + ? ) and V?? ?

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