- #1

TheFallen018

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Hey, I've got this problem that I've been trying to crack for a while. I can't find any info for multi-variable expected values in my textbook, and I couldn't find a lot of stuff that made sense to me online. Here's the problem.

View attachment 8906

I tried to get the limits from the normal distributions that were given. If I was doing it right, I had

$90\leq X \leq 130 $

$1.9\leq Y \leq 2.9$

for X and Y.

I think my main problem is that I'm not sure how to get $f(x)$ and $f(y)$ so that I can use the property

$E(aX+bY) = aE(X)+bE(Y)$

and

$E(x) = \int_{n}^{m}x*f(x)dx$

where $n \leq f(x) \leq m$.

I think I might be able to figure it out once I can work out what the functions should be, but I'm a little stuck here. Any help would be awesome. Thanks.

View attachment 8906

**Find $E(C)$****Find $Var(C)$**I tried to get the limits from the normal distributions that were given. If I was doing it right, I had

$90\leq X \leq 130 $

$1.9\leq Y \leq 2.9$

for X and Y.

I think my main problem is that I'm not sure how to get $f(x)$ and $f(y)$ so that I can use the property

$E(aX+bY) = aE(X)+bE(Y)$

and

$E(x) = \int_{n}^{m}x*f(x)dx$

where $n \leq f(x) \leq m$.

I think I might be able to figure it out once I can work out what the functions should be, but I'm a little stuck here. Any help would be awesome. Thanks.

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