Compute the probability

1. Let
2. If X is N(1, 4), compute the probability
3. If X is N(75, 25), find the conditional probability that X is greater than 80 given that X is greater than 77. See Exercise 2.3.12.

Exercise 2.3.12

Let and denote, respectively, the pdf and the cdf of the random variable X. The conditional pdf of , given a fixed number, is defined This kind of conditional pdf finds application in a problem of time until death, given survival until time .