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Question
"Here is the problem I am working on:
An appliance dealer sells three different models of upright
freezers having 13.5, 15.9, and 19.1 cubic feet of storage
space. Let X = the amount of storage space purchased by the
next customer to buy a freezer. Suppose that X has pmf
x |13.5 15.9 19.1
------------------------
p(x)| .2 .5 .3
a) Compute E(X),E(X^2), and V(X).
E(X) = The Expected Value of a Function
E(X^2) = Same thing just squared?(Not Sure)
V(X) = The Variance of X
The answers I got for the first two are:
E(X) = 40.68
E(X^2) = 59.694
I don't know if either of those are right and I can't
figure out how to find the V(X).
b)If the price of a freezer having capcity X cubic feet is
25X-8.5, what is the expected price paid by the next
customer to buy a freezer?
c)What is the variance of the price 25X-8.5 paid by the ext
customer?
d) Suppose that although the rated capacity of a freezer is
X, the actual capacity is h(X) = X - .01X^2. What is the
expected actual capacity of the freezer purchased by the
next customer?
Thanks for any help you can provide the book I'm using is
very technical and I am having hard time following it along
with the massive amounts of notation it's throwing at me.
Thanks for the help I really appreciatte it!"
a) To get the expected value, take each x (13.5, 15.9, and 19.1)
times each p (0.2, 0.5, and 0.3) and add the results up.
That should be 0.2*13.5 + 0.5*15.9 + 0.3*19.1.
To find the E(x²), you're right.
Add up 0.2*13.5² + 0.5*15.9² + 0.3*19.1².
The variance is given by E(x²)-E(x)².
b) Take formula P(X) = 25X-8.5 and evaluate
0.2*P(13.5) + 0.5*P(15.9) + 0.3*P(19.1)
to get the expected price.
c) This is calculated in the same way as the variance was
calculated in the first problem, but using the price of
each of the sizes. You found the expected value of the
price in the last equation. Square the price { P²(x) } and
still multiply by the same percentage for each one.
Add these terms up and compute the variance as E(P(x)²)-E(P(x))².
d) Take the 13.5, 15.9 and 19.1 and put them into the equation
h(x) = X - 0.01*X², multiplying each of them by 0.2, 0.5, and 0.3.
Add them up as this is done.
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Scott A Wilson
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