# 3.5.8

#### kbor2259

##### New member
Find E(Y) of fy= (3/4) 0<y<1
(1/4) 2<y<3
0 elsewhere
the < should be less than or equal to

#### tkhunny

##### Moderator
Staff member
If we get to use calculus, I'd evaluate this:

$$\displaystyle \int_{-\infty}^{\infty} y\cdot f_{Y}\;dy$$

Of course, I would also check for validity by verifying:

$$\displaystyle \int_{-\infty}^{\infty} f_{Y}\;dy$$ = 1

Without the calculus, the geometry is not difficult.

$$\displaystyle \frac{1}{2}\cdot\frac{3}{4} + \frac{5}{2}\cdot\frac{1}{4}$$

Unique answers don't care how you find them.