An Appliance Dealer Sells Three Different Models of Upright Freezers $$\begin{array} { l c c c } \hline x & 13.5 & 15.9 & 19.1 \\\hline P ( x ) & .2 & .4 & .4 \\\hline\end{array}$$

question 3

Essay

An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has pmf $$\begin{array} { l c c c } \hline x & 13.5 & 15.9 & 19.1 \\\hline P ( x ) & .2 & .4 & .4 \\\hline\end{array}$$
a. Compute $E ( X ) , E \left( x ^ { 2 } \right) , \text { and } V ( X )$
b. If the price of a freezer having capacity 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 next customer?
d. Suppose that although the rated capacity of a freezer is X, the actual capacity is $h ( X ) = X - .01 X ^ { 2 }$
What is the expected actual capacity of the freezer purchased by the next customer?

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Definitions:

Applied Research

Applied research is focused on solving practical problems or developing new technologies, as opposed to theoretical or basic research.

Hindsight Bias

The habit of assuming that one would have foretold the result following the occurrence of an event.

Critical Thinking

The objective analysis and evaluation of an issue to form a judgment, often involving questioning assumptions and identifying biases.

Overconfidence

A cognitive bias characterized by an individual's overestimation of their own abilities, performance, or level of control.