A continuous random variable X has cumulative function distrubution F(x)= a  , x<01/2x+b  , 0<x<2c  x >2Determine: i. the values of a,...

A continuous random variable X has cumulative function distrubution 

F(x)= a  , x<0

1/2x+b  , 0<x<2

c  x >2

Determine: 

i. the values of a, b, and c

ii. the probability density function of X, 

iii. the expected value of X

iv. the standard deviation of X

v. P(0.5<X<3))

vi. the median