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2 years ago

The popcorn in a vending machine costs $0.75 per bag. Which function rule describes the situation?

Mathematics

1 answer:

BabaBlast [244]2 years ago

5 0

Answer:

f(b)=75%b

hope it helped :)

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Digiron [165]

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

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Using the same variance identity, we have

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

and

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so that

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Alternatively, we can use the identity

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

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