Let X be an exponential(l) random variable, and define Y to be the integer part of X 1, that is Y i 1 if and only if i X i 1, i 0, 1, 2, (a) Find the distribution of Y What well known distribution does Y have (b) Find the conditional distribution of X 4 given Y 5

Question: Let X be an exponential(l) random variable, and define Y to be the integer part of X + 1, that is Y = i +

Let X be an exponential(l) random variable, and define Y to be the integer part of X + 1, that is
Y = i + 1 if and only if i < X < i + 1, i = 0, 1, 2,
(a) Find the of Y. What well-known does Y have?
(b) Find the conditional of X - 4 given Y > 5.

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