My professor gave us these problem and I can't solve it. He didn't really explain well the lesson on normal distribution so I'm just so lost with this. Hope somebody can help.

1.) Let X be a continuous random variable defined on the interval [0, 2]. The PDF of X is given by
$\displaystyle f(x)= \frac 1 2 X$
a. Graph the PDF of X
b. Find P(X>1.5)
c. Find P(X≤1.5)
d. Find P(0.5<X<1.5)

2. The function is just 0 until you reach the origin, then
it's x/2 until the point (2,1) then at 2 it's zero again.
Now you really should find the cdf instead.
However $\displaystyle P(X>1.5)=\int_{3/2}^2 x/2 dx$
While $\displaystyle P(X\le .5)=1-P(X>1.5)$
Finally $\displaystyle P(.5<X<1.5)=\int_{1/2}^{3/2} x/2 dx$

3. Originally Posted by matheagle
The function is just 0 until you reach the origin, then
it's x/2 until the point (2,1) then at 2 it's zero again.
Now you really should find the cdf instead.
However $\displaystyle P(X>1.5)=\int_{3/2}^2 x/2 dx$
While $\displaystyle P(X\le .5)=1-P(X>1.5)$
Finally $\displaystyle P(.5<X<1.5)=\int_{1/2}^{3/2} x/2 dx$
thanks. but i don't understand. sorry. can you please explain more?