# Not the Uniform Distribution

• Feb 24th 2010, 01:37 PM
aaronrj
Not the Uniform Distribution
Let X have the following CDF:

http://www.utdallas.edu/%7Embaron/33...s/image008.gif

(a)Find the PDF f(x).
(b)Find P(1 < X < 1.5).
• Feb 24th 2010, 03:07 PM
chabmgph
Quote:

Originally Posted by aaronrj
Let X have the following CDF:

http://www.utdallas.edu/%7Embaron/33...s/image008.gif

(a)Find the PDF f(x).
(b)Find P(1 < X < 1.5).

The PDF is the derivative of your CDF. Use this fact to get started.
And you can either use your CDF or PDF to calculate part (b). (Think about what it is asking)
• Feb 24th 2010, 04:37 PM
aaronrj
so would i just find the derivative of 1/8x + 3/16x^2 and plug in for F(b)-F(a)? In which case it would be 1/8 + 3/16x = 1/8 + 3/16(2) - 1/8+3/16(0)= 3/8?
• Feb 24th 2010, 08:24 PM
CaptainBlack
Quote:

Originally Posted by aaronrj
so would i just find the derivative of 1/8x + 3/16x^2 and plug in for F(b)-F(a)? In which case it would be 1/8 + 3/16x = 1/8 + 3/16(2) - 1/8+3/16(0)= 3/8?

The derivative of \$\displaystyle F(x)\$ is the density.

The probability \$\displaystyle P(a<X<b)=F(b)-F(a)\$

CB