Answered: An certain brand of upright freezer is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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$### Problem Statement: A certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft³, and 20 ft³. Let $X$ represent the rated capacity of a freezer of this brand sold at a certain store. Suppose that $X$ has the following probability mass function (pmf): | $x$ | 16 | 18 | 20 | |------------|----|----|----| | $p(x)$ | 0.3| 0.1| 0.6| #### (a) Compute $E(X)$, $E(X^2)$, and $V(X)$. $ \\ E(X) = $ _______________ ft³ \\ $E(X^2) = $ _______________ ft³ \\ $V(X) = $ _______________ ft³ \\ #### (b) If the price of a freezer having capacity $X$ is $68X - 650$, what is the expected price paid by the next customer to buy a freezer? \$ ______________ #### (c) What is the variance of the price paid by the next customer? ______________ #### (d) Suppose that although the rated capacity of a freezer is $X$, the actual capacity is $h(X) = X - 0.009X^2$. What is the expected actual capacity of the freezer purchased by the next customer? (Enter your answer to four decimal places.) _____________ ft³$

Transcribed Image Text:### Problem Statement: A certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft³, and 20 ft³. Let $X$ represent the rated capacity of a freezer of this brand sold at a certain store. Suppose that $X$ has the following probability mass function (pmf): | $x$ | 16 | 18 | 20 | |------------|----|----|----| | $p(x)$ | 0.3| 0.1| 0.6| #### (a) Compute $E(X)$, $E(X^2)$, and $V(X)$. $ \\ E(X) = $ _______________ ft³ \\ $E(X^2) = $ _______________ ft³ \\ $V(X) = $ _______________ ft³ \\ #### (b) If the price of a freezer having capacity $X$ is $68X - 650$, what is the expected price paid by the next customer to buy a freezer? \$ ______________ #### (c) What is the variance of the price paid by the next customer? ______________ #### (d) Suppose that although the rated capacity of a freezer is $X$, the actual capacity is $h(X) = X - 0.009X^2$. What is the expected actual capacity of the freezer purchased by the next customer? (Enter your answer to four decimal places.) _____________ ft³

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