Question: A random variable X with a mean of 2.5 follows an exponential distribution. Find the following probabilities: (a) P(X > 2.5), (b) P(X < 1),

A random variable X with a mean of 2.5 follows an exponential distribution. Find the following probabilities:

(a) P(X > 2.5),

(b) P(X < 1), and

(c) P(0.5 < X < 1.5). Find the values of x0 if

(d) P(X < x0) =

0.1, and

(e) P(X > x0) = 0.05.

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