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Name: A farmer has 60 lbs of apples and120 lbs of potatoes for sale. The mar
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Description: A farmer has 60 lbs of apples and120 lbs of potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0.8 dollars and a standard deviation of 0.3 dollars. Similarly, for a pound of potatoes, the mean p

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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A farmer has 60 lbs of apples and120 lbs of potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0.8 dollars and a standard deviation of 0.3 dollars. Similarly, for a pound of potatoes, the mean price is 0.7 dollars and the standard deviation is 0.1 dollars. It also costs him 5 dollars to bring all the apples and potatoes to the market. The market is busy with shoppers, so assume that he'll be able to sell all of each type of produce at that day's price. Complete parts a) through d). Make sure to consider all necessary assumptions before calculating.

a) Define your random variables, and use them to express the farmer's net income.

b) Find the mean.

The mean profit is

nothing

dollars.

c) Find the standard deviation of the net income.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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