1. The time (in hours) required to repair a machine is an exponentially distributed random variablewith parameter λ = 1/4.

(a) What is the probability that a repair time exceeds 4 hours.

(b) What is the conditional probability that a repair takes at least 10 hours, given that its duration exceed 9 hours.

For a) I got the answer $\displaystyle 1 - e^{-1}$

How do you do b)?

Is it $\displaystyle P(X>=10) = 1 - P(X<=9)? $

2. An electronic equipment is used to measure brain mass. If the brain mass for a randomly selected person is m grams, the machine measures and amount Y , where Y = m + X and X is normally distributed with mean 0 and variance 4. What is the probability that the measure Y does not deviate from the true value m by more than 1.3 grams?

Thank you very much!