Analyzing a Distribution Function

[twoski]

Homework Statement

The distribution function of a real random variable X is given:

F(x) =

0 : x < 0
x/2 : 0 ≤ x < 1
2/3 : 1 ≤ x < 2
11/12 : 2 ≤ x < 3
1 : 3 ≤ x

(a) Plot this distribution function.
(b) What is P( X > 1/2 ) ?
(c) What is P( 2 < X ≤ 4 ) ?
(d) What is P( X < 3 ) ?
(e) What is P( X = 1 ) ?

The Attempt at a Solution

Plotting was easy, but now I'm just unsure of my answers to the others.

P( 2 < X < 4 ) = 1 - 2/3 = 1/3
P( X = 1 ) = 2/3
P( X > 1/2 ) = ? This one confuses me.
P( X < 3 ) = F(0) + F(1) + F(2) ? Not sure if i need to be subtracting something here since this is wrong.

 

[Karnage1993]

For (b), use the fact that $P(X > x) = 1 - P(X \le x)$.

 

[twoski]

Ah, so it would essentially be 1 - P(x ≤ 1/2) which translates to 1 - 0.25 = 0.75, right?

 

[twoski]

For question (d) would i just do the opposite of your formula and subtract 1 from P( X >= x )?