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 Ywith a density function given by i f= yz' V2\" 0, elsewhere, where b is the minimum possible time needed to traverse the maze. (a) Show that y) has the properties of a density function. Consider y z b. Since 13 represents the minimum time needed to traverse the maze, we can conclude b >l . Then since y 2 b, we know y2 > and f(y) = i2 l 7 v 0. Since f(y) = D for y b + c) for a positive constant 5. PO\" > b + c) = ' ' (d) If c and d are both positive constants such that d > c, find P(Y > b + d|Y > b + c). P(Y>b+d|Y>b+c)=