1. ## Random Variables

Let X be the number of heads in 20 fair coin tosses, Y a number picked uniformly at random from {0,1,...,20}, independently of X. Let Z=max (X,Y).

a) Find a formula for P(Z=k), k=0,...,20.

b) Without calculating out P(Z=k) exactly, sketch the histogram of Z, and explain its unusual shape.

2. Originally Posted by Yan
Let X be the number of heads in 20 fair coin tosses, Y a number picked uniformly at random from {0,1,...,20}, independently of X. Let Z=max (X,Y).

a) Find a formula for P(Z=k), k=0,...,20.

b) Without calculating out P(Z=k) exactly, sketch the histogram of Z, and explain its unusual shape.
The ideas you need are order statistics for discrete random variables.

3. Originally Posted by mr fantastic
The ideas you need are order statistics for discrete random variables.
that's the part that i don't get it.
I prefer you show me step by step not just give me a "hint".
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