Suppose X and Y are independent Binomial random variables, each with n=3 and p=9/10.
a. Find the probability that X and Y are equal, i.e., find P(X=Y).
b. Find the probability that X is strictly larger than Y, i.e., find P(X>Y).
c. Find the probability that Y is strictly larger than X, i.e., find P(Y>X).
a) The probability here is computed as:
Therefore 0.5912 is the required probability here.
b) Now there are two possibilities here, either X > Y or Y > X in case where X is not equal to Y.
P(X not equal to Y) = 1 - P(X = Y) = 1 - 0.5912 = 0.4088
Therefore due to symmetry we would have: P(X > Y) = P(Y > X) = 0.4088 / 2 = 0.2044
Therefore 0.2044 is the required probability here.
c) As explained in the previous part itself, P(X > Y) = P(Y > X) = 0.2044
Therefore 0.2044 is the required probability here.
Suppose X and Y are independent Binomial random variables, each with n=3 and p=9/10. a. Find...
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