Consider a statistical expirement of flipping a pair of fair coins simultaneously. Let X & Y...

Consider a statistical expirement of flipping a pair of fair coins simultaneously. Let X & Y be the number heads in flipping each coin.

Define a joint density function Z = XY. (I provided the answers in bold but I need help understanding how it is solved. Thank you in advance).

a) The number of possible distinct values of Z is: 2

b) The probability of Z = 0 is: 3/4

c) The mean of Z is: 1/4

d) The standard deviation of Z is: sqrt(3/16)

e) The correlation coefficient of X and Y is: 0

f) Which RV follows a uniform distribution among all three random variables, X, Y, and Z? X & Y

Expert Solution

f. If all values of random variable have same probability then that random variable has uniform distribution.

X and y having equal probability for its all values but z does not.

Hence X and Y follow uniform distribution.

orchestra answered 1 year ago

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