Question

Please show work and explain! I am very confused.

10. (TR) Let X be a random variable with cumulative distribution function 125 t〉5 2 t〈2 Fx(t) = 〈 0.2 + 0.1t, K 5 . 0.1 3-t

Answer 1

here from above at break points :at P(X<2)=0.1/(3-2)=0.1

P(X=2)=P(X<=2)-P(X<2)=(0.2+0.1*2)-(0.1/(3-2))=0.4-0.1=0.3

P(X<=2)=(0.2+0.1*2) =0.4

P(X<5)=0.2+0.1*5=0.7

P(X=5)=P(X<=5)-P(X<5)=(1-1/5²)-(0.2+0.1*5)=0.96-0.7=0.26

P(X<=5)=(1-1/5²)=0.96

Xiii) let 60 th percentile =a

as from above it is between 40 th and 70 th percentile

0.2+0.1*a=0.6

a=4

xiv)

0.2+0.1*a=0.5

a=3

xv)

for 99th percentile is above 96th percentile:

1-1/a² =0.99

1/a² =0.01

a²=100

a=10

xvi) 0.1/(3-t)=0.04

3-t=2.5

t=0.5