sellers bring items to an auction house where buyers may bidfor them. experience

Question

sellers bring items to an auction house where buyers may bidfor them. experience has hown that the mean selling price of an article is =$100.the auction house charges $10 for storage of each item and takes an additional 15%commission on each sale. let X denote the amount returned to the seller. find the expected value ofX. **i know the answer is $75, however dont know how to getit** sellers bring items to an auction house where buyers may bidfor them. experience has hown that the mean selling price of an article is =$100.the auction house charges $10 for storage of each item and takes an additional 15%commission on each sale. let X denote the amount returned to the seller. find the expected value ofX. **i know the answer is $75, however dont know how to getit**

Explanation / Answer

Let us define the variables

X : selling price of each item

Y : amount returned to the seller

Now from the question we know that

E(X) = $ 100

We also have the relationship

Y = X – 10% * X – 15%* X

ð Y= 0.75 X

Now Expected value of Y denoted as E(Y ) = E(0.75* X)

ð E(Y) = 0.75 * E(X)   (we can pull out constants out ofthe Expectation function)

ð E(Y) = 0.75* 100 = 75

Feel free toask for any clarifications. Hope it helps you

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