What I gather from the question is that $X$ has second moment $E(X^2)=81$ and variance $V(X) = 58$ , and you're asked to find the expectation and variance of the random variable $Y=2X+10$ .

From the given second moment and variance, we find the expectation of $X$ :

$V(X) = E(X^2) - E(X)^2 \implies E(X) = \sqrt{E(X^2) - V(X)} = \sqrt{23}$

Expectation is linear, so

$E(Y) = E(2X+10) = 2 E(X) + 10 = \boxed{2\sqrt{23} + 10}$

Using the same variance identity, we have

$V(Y) = V(2X+10) = E((2X+10)^2) - E(2X+10)^2$

and

$E((2X+10)^2) = E(4X^2 + 40X + 100) = 4E(X^2) + 40E(X) + 100 = 424 + 40\sqrt{23}$

so that

$V(Y) = V(2X+10) = (424 + 40\sqrt{23}) - (2\sqrt{23} + 10)^2 = \boxed{232}$

Alternatively, we can use the identity

$V(aX+b) = a^2 V(X) \implies V(2X+10) = 4V(X) = 232$

5 0

2 years ago

I need the answer cause this is for a grade please!!! Jamie has a rectangular room in her home with a width of 8 feet and a diag

FinnZ [79.3K]

Answer:

You can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

92+72−−−−−−√=11.4

Step-by-step explanation:

4 0

3 years ago

A literal equation has only one variable. True False

Zanzabum

Answer:False

Step-by-step explanation:

5 0

3 years ago

Please help ASAP!

marusya05 [52]

Answer:

Not a function

Step-by-step explanation:

This is not a function because there are different outputs for the same input.

8 0

3 years ago

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