An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the ra
ted capacity of a freezer of this brand sold at a certain store. Suppose that X has the following pmf. x 16 18 20
p(x) 0.3 0.1 0.6
(a) Compute E(X), E(X2), and V(X).
(b) If the price of a freezer having capacity X is 60X − 650, what is the expected price paid by the next customer to buy a freezer?
The expected price paid by the next customer to buy a freezer is $466
Step-by-step explanation:
From the information given we know the probability mass function (pmf) of random variable X.
<em>Point a:</em>
The Expected value or the mean value of X with set of possible values D, denoted by <em>E(X)</em> or <em>μ </em>is
Therefore
If the random variable X has a set of possible values D and a probability mass function, then the expected value of any function h(X), denoted by <em>E[h(X)]</em> is computed by
So and
The variance of X, denoted by V(X), is
Therefore
<em>Point b:</em>
We know that the price of a freezer having capacity X is 60X − 650, to find the expected price paid by the next customer to buy a freezer you need to:
From the rules of expected value this proposition is true:
We have a = 60, b = -650, and <em>E(X)</em> = 18.6. Therefore
Firstly, you would subtract 7 from both sides, leaving you with 3m=21. You would then divide by three in order to be left with total value of m. 3m divided by 3 is m. 21 divided by 3 is 7. Therefore m=7 :)