2.21. Let X and Y be independent Bernoulli (1/2) random variables. Let Z - (Y – X)². What is the distribution of Z? Show that Z and X are independent. Show that Z and Y are also independent, but that X, Y and Z are not independent.

Q: Please can you maybe snap, I can't quite understand the way you typed it thanks

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A: Apply integration by parts:

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A: The mean is $31,000, standard deviation is $3000.

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Q: Please solution for part G,  Thanks!

A: (g) n=50, P(∑i=150Xi&lt;1124.54)=?

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Q: could you provide an example please?

A: Let us take:  u→=0, 0, 0v→=1, 2, 3w→=4, 5, 6

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A: Doubt: How did you figure out the answers.

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Q: Can you draw a table so I can understand better

A: Start with a in the column one and make possible pairs. Then go with b, then c and then so on.