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Math Help - Random Variables

  1. #1
    Yan
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    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.
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  2. #2
    Flow Master
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    Quote Originally Posted by Yan View Post
    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.
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  3. #3
    Yan
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    Quote Originally Posted by mr fantastic View Post
    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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