# Plotting a Distribution

1. Feb 25, 2013

### twoski

1. The problem statement, all variables and given/known data

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 ) ?

3. 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.

2. Feb 25, 2013

### Karnage1993

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

3. Feb 25, 2013

### twoski

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

4. Feb 28, 2013

### twoski

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