Question: 4. Consider X is a Exponential random variable with mean . Find out and sketch the probability distri- butions of a) Y = 1 b)

4. Consider X is a Exponential random variable with mean . Find out and sketch the probability distri- butions of a) Y = 1 b) Y = X . 1[X 0. Also find mean and variance of Y c) Y = X . 1[X E (a, b] for some b > a > 0. Note: 1(.) is an indicator function

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