Thread: Cumulative Distribution Function Question

The C.D.F. (cumulative density function) of the random variable X is given by,

F(x)= [0, x<0
x/2, 0<=x<1
2/3, 1<=x<2
11/12, 2<=x<3
1, 3<=x]

a) Find P(X>1/2)

b) Find P(2<X<=4)

c) Find P(X=1)

Does anyone know how to approach this?

Originally Posted by abc4616

The C.D.F. (cumulative density function) of the random variable X is given by,

F(x)= [0, x<0
x/2, 0<=x<1
2/3, 1<=x<2
11/12, 2<=x<3
1, 3<=x]

a) Find P(X>1/2)

Definition of the cdf, tells you that:

P(X>1/2)=F(1/2).

b) Find P(2<X<=4)

Again from the definition of the sdf:

P(2<X<=4)=P(X<=4)-P(X<2)=F(4)-F(2)

c) Find P(X=1)

This is equal to the jump in the cdf at x=1, so its F(1)-F(1-)=2/3-1/2=1/6

RonL