f(y)={((b)/(y^(2)),y>=b),(0, elsewhere ):}

\ where

b

is the minimum possible time needed to troverse the maze.\ (a) Show that

f(y)

has the properties of a density function.\ Consider

y>=b

. Since

b

represents the minimum time needed to traverse the maze, we can conclude

b>

Then since

y>=b

, we know

y^(2)>

and

f(y)=(b)/(y^(2))>=v,0

. Since

f(y)=0

for

f(y)>=v,0y\\\\int_(-\\\\infty )^- f(y)dy=F(y)P(Y>b+c)cP(Y>b+c)=y by definition we know f(y)>=v,0 for all y. together these show \\\\int_(-\\\\infty )^- f(y)dy=\ (b) Find F(y).\ (c) Find P(Y

)

>

(

b+c) for a positive constant c.\ P(Y>b+c)=

f(y)={y2b,0,ybelsewhere where b is the minimum possible time needed to traverse the maze. (a) Show that f(y) has the properties of a density function. Consider yb. Since b represents the minimum time needed to traverse the maze, we can conclude b> . Then since yb, we know y2> and f(y)=y2b>v0. Since f(y)=0 for yb+c) for a positive constant c. P(Y>b+c)=