Random variables X and Y are independent if Prob[X = x and Y = y] = Prob[X = x] Prob[Y = y]. Show that this implies that knowing the value of variable tells you nothing about the value of the other: Prob[X = x |Y = y1] = Prob[X = x]. Show that if X and Y are independent, then Var[X + Y] = Var[X] + Var[Y]. Consider rolling n dice and adding their tops to give a number between n and 6n. What is the expectation, what is the variance, and what is the standard deviation?

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