The amount of wait time for a bus is a random variable X with probability density function f(x) ={ 1/15 , if 0x5 or 2/5-1/25x, if 5x10 a. Show...

The amount of wait time for a bus is a random variable X with probability density function

f(x) ={ 1/15 , if 0<x<5 or 2/5-1/25x, if 5<x<10

a. Show that f(x)  is a valid pdf.

 i know that to be a valid pdf the integaral of f(x) from - infinity to infinity has to equal 1, but when i integrated from o to 5 + from 5 to 10 i got 0.7 not 1

b. Determine the equation of the CDF function

F(X) = 1/25 for 0<= x <5 , and 2/5x - x^2/50 of 5<= x <10 is that right?

c. Use the CDF function, find p(X<2.5)

 =1/10 is that right?

d. Use the CDF function, find .P(X > 7)

= 91/50 is that right?