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A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x)=√x, 0

A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x)=√x, 0

MATLAB: An Introduction with Applications
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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Parts A (I, ii, iii
(c) A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x) = ³√x, 0<x< 1. (i) According to the model, what is the mean length of the sticks that the scout brings back? (ii) According to the model, what is the standard deviation of the lengths of the sticks that the scout brings back? (iii) What are the units of the mean and the standard deviation that you have just calculated? (d) The number of customers buying a cooked breakfast at a high-street cafe on a weekday morning is a random variable X with mean 24 and variance 36. As a loss leader - a product sold at a loss to attract customers to also partake of its other offerings - the cafe charges £3.50 per breakfast and has fixed breakfast-specific daily costs (ingredients, labour) of £105. Let Y be the cafe's daily loss on breakfasts, in pounds, where Y = 105 3.5X. What are the mean and standard deviation of this loss?
Transcribed Image Text:(c) A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x) = ³√x, 0<x< 1. (i) According to the model, what is the mean length of the sticks that the scout brings back? (ii) According to the model, what is the standard deviation of the lengths of the sticks that the scout brings back? (iii) What are the units of the mean and the standard deviation that you have just calculated? (d) The number of customers buying a cooked breakfast at a high-street cafe on a weekday morning is a random variable X with mean 24 and variance 36. As a loss leader - a product sold at a loss to attract customers to also partake of its other offerings - the cafe charges £3.50 per breakfast and has fixed breakfast-specific daily costs (ingredients, labour) of £105. Let Y be the cafe's daily loss on breakfasts, in pounds, where Y = 105 3.5X. What are the mean and standard deviation of this loss?
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