Suppose X follows a continuous uniform distribution from 1 to 4,Determine the conditional probability

Upper P left parenthesis Upper X greater than 2.5 | Upper X less than or equals 3 right parenthesis

2)

A bus arrives every 20minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.

(a) What is the probability that the individual waits more than 14minutes?

(b) What is the probability that the individual waits between 8 and 14minutes?

3)

The life, in years, of a certain type of electrical switch has an exponential distribution with an average life beta =4. If 400 of these switches are installed in different systems, what is the probability that at most 75 fail during the first year?

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