1 - X
P(1 - X = 1) = P(X = 0) = 1 - 0.2 = 0.8
P(1 - X = 0) = P(X = 1) = 0.2
Thus, 1 - X ~ B0.8
The parameter is 0.8
X2
P(X2 = 1) = P(X = 1) = 0.2 as, X cannot be negative
P(X2 = 0) = P(X = 0) = 0.8
X2 ~ B0.2
The parameter is 0.2
X.Y
P(X.Y = 1) = P(X = 1) * P(Y = 1) = 0.2 * 0.35 = 0.07
P(X.Y = 0) = 1- P(X.Y = 1) = 1 - 0.07 = 0.93
X.Y ~ B0.07
The parameter is 0.07
|X - Y|
|X - Y| can take only values 0 and 1.
P(|X - Y| = 1) = P(X = 1) * P(Y = 0) + P(X = 0) * P(Y = 1) = 0.2 * (1 - 0.35) + (1 - 0.2) * 0.35 = 0.41
P(|X - Y| = 0) = 1 - 0.41 = 0.59
X + Y
X + Y = 2 when X = Y = 1. Thus, X + Y is not a Bernoulli random variable.
The answer is -1
If X and Y are Bernoulli random variables with parameters 0.2 and 0.35, which means X~Bo.2...
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