stats............................

1. [1|] Marks} As a measure of intelligence. mice are timed when going through a maze to reach a reward of food. The time {in seconds] required for any mouse is a random variable Y with a density function given by yi={ if: gab? where b is the minimum possible time needed to traverse the maze. a} Show that y} has the properties of a density function. h} Find F{y}. c} Find P{Y :3 h + c) for a positive constant c. d} if c and d. are both positive constants such that d. 3:- c1 nd Pr' :1: bI till\" 1':- b+ c}. 2. [1|] Marks] Weekly ISPU time used by an accounting rm has probability density function{n1easured in hours} given by _ {Brew y). u s y s 4. fly} { . elsewhere. :1} Find the expected value and variance of weeka CPU time. b} The CPU time costs the rm $20!) per hour. Find the expected value and variance of the weekly cost for CPU time. c} Would you expect the weekly cost to exceed $60G very often? Why