Math Help - [SOLVED] need help on stats, plz!

1. [SOLVED] need help on stats, plz!

I need help with following questions plz, really appreciate it

2. The density is $f(y)=1-y$ on 0<y<1 and $f(y)=.5$ on 2<y<3.

Now you need $\int_0^3 yf(y)dy$ and $\int_0^3 y^2f(y)dy$.

3. Sorry to bother you again, how do u find and ? can u provide me the solution for the questions? thanks

4. basic calculus one

$\int_0^3 yf(y)dy= \int_0^1 (1-y)ydy + .5\int_2^3 ydy$

and

$\int_0^3 y^2f(y)dy= \int_0^1 (1-y)y^2dy + .5\int_2^3 y^2dy$.

5. The CDF is zero if y<0

$\int_0^y (1-t)dt= y-y^2/2$ on 0<y<1

.5 on 1<y<2

$.5 + .5\int_2^y dt =.5 + .5(y-2)=.5y-.5$ on 2<y<3

and 1 after 3.

You can put include the endpoints of each interval anywhere you wish.