Statistics

1. The length of time (in hours) required by a student to complete an exam can be modeled by a random variable Y with a density given by M) = gay/2 if y > 0, and 0 otherwise. (a) (2 pts) What is the distribution of Y? Specify its name and parameter(s). (b) (2 pts) Find the expected value and variance for the amount of time that it will take for the student to nish the exam. (c) (2 pts) Given that the student needs at least 30 minutes to complete the exam, nd the probability that the student will require at least 60 minutes to nish. ((1) (2 pts) Suppose there is a student who needs 50% more time to nish the exam. Let X = 1.5Y be the length of time (in hours) that this student needs to nish the exam. Find the mean and variance of X using the properties of expectation and variance