I have a random variable Y, which is defined by:

```
$$ Y = aX_1 + bX_2 $$
```

Where we know `$ X_1 $`

Y `$ X_2 $`

They are independent. How do I write? `$ EX_1 $`

Y `$ EX_2 $`

in terms of only *a*, *second*, *EY*, and Var*Y*?

I have already written the expectation of Y to the following expectation properties:

```
$$ EY = aEX_1 + bEX_2 $$
```

and to obtain `$ EX_1 $`

I can write `$ frac {EY = bEX_2} {a} $`

; however, how would I get rid of the `$ EX_2 $`

? Essentially, I can write the expectations of the linear combinations, but I have no idea how to write each individual expectation within that linear combination without using the other variables in that combination.

Finally, how could you solve the expectation of `$ X_i $`

for a general form `$ Y = a_1X_1 + ... + a_iX_i $`

only in terms of `$ a_ {1, ..., i} $`

, EY, and VarY?

Thank you!

PS This is my first Stack post, and I was wondering how to get everything to appear in Latex.