Random Variables

• Oct 26th 2008, 05:52 PM
Yan
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.
• Oct 27th 2008, 04:31 AM
mr fantastic
Quote:

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.
• Oct 28th 2008, 05:51 PM
Yan
Quote:

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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