# density function

• Sep 3rd 2007, 12:32 PM
nisoo-1
density function
Q#1 A continuous random variable X has the density function
f(x)=x for 0<x<1
2-x for 1_<x<2
0 elsewhere

a. Show that P(0<X<2)=1
b. Find P(X<1.2).
• Sep 4th 2007, 12:00 AM
CaptainBlack
Quote:

Originally Posted by nisoo-1
Q#1 A continuous random variable X has the density function
f(x)=x for 0<x<1
2-x for 1_<x<2
0 elsewhere

a. Show that P(0<X<2)=1

$
P(0$

RonL
• Sep 4th 2007, 12:05 AM
CaptainBlack
Quote:

Originally Posted by nisoo-1
Q#1 A continuous random variable X has the density function
f(x)=x for 0<x<1
2-x for 1_<x<2
0 elsewhere

b. Find P(X<1.2).

$
P(x<1.2) = \int_0^{1.2} f(x) ~dx = \int_0^1 x ~dx + \int_1^{1.2} (2-x)~dx = 1/2 + \left[ 2x-x^2/2\right]_1^{1.2}$

RonL
• Sep 9th 2007, 07:52 PM
TKHunny
Calculus may be a bit much for this problem. If you are supposed to use it, fine, but please keep in mind there may be other ways of going about things. In this case, if you know a little about right triangles it is just as straight-forward.