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The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are hundreds of calories).

The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are hundreds of calories).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are hundreds of calories). 5.13 3. (x – 2)(6 – x), 2<x < 6 32 (x)S (), otherwise. Find the mean, variance, and standard deviation of the distribution of the daily total solar radiation in Tampa in October. The "on" temperature of a thermostatically controlled switch for an air-conditioning system is set at 72°, but the actual temperature X at which the switch turns on is a random variable having the probability density function 5.14 う,71<x<73 = (x)S (), otherwise. Find the mean and standard deviation of the distribution of the temperatures at which the switch turns on.
Transcribed Image Text:The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are hundreds of calories). 5.13 3. (x – 2)(6 – x), 2<x < 6 32 (x)S (), otherwise. Find the mean, variance, and standard deviation of the distribution of the daily total solar radiation in Tampa in October. The "on" temperature of a thermostatically controlled switch for an air-conditioning system is set at 72°, but the actual temperature X at which the switch turns on is a random variable having the probability density function 5.14 う,71<x<73 = (x)S (), otherwise. Find the mean and standard deviation of the distribution of the temperatures at which the switch turns on.
5.15 The weekly repaikcost, X , for a certain machine has a probability density function given by бx (1 — х), 0<x<1 0 <x < 1 - f (x). = 0, :0.75= one- otherwise with measurements in $100s. or Find the mean and variance of the distribution of repair costs. Find an interval within which these weekly repair costs should lie at least 75% of the time using Tchebysheff's Theorem. Find an interval within which these weekly repair costs lie exactly 75% of the time with exactly half of those not lying in the interval above the upper limit and the other half below the lower limit. Compare this interval to the one obtained in part (b). 5.16 In a genetics study, it was found that the distance X between mutations in a certain strand of DNA had a probability density function given by te-x/5, x > 0 f (x) : 0, otherwise with measurements in kb. a Find the mean and variance of the distribution of distances between mutations in this strand of DNA. Find an interval within which these distances between mutations should lie at least 75% of the time using Tchebysheff's Theorem. Find an interval within which these distances between mutations lie exactly 75% of the time with exactly half of those not lying in the interval above the upper limit and the other half lying below the lower limit. Compare this interval to the one obtained in part (b).
Transcribed Image Text:5.15 The weekly repaikcost, X , for a certain machine has a probability density function given by бx (1 — х), 0<x<1 0 <x < 1 - f (x). = 0, :0.75= one- otherwise with measurements in $100s. or Find the mean and variance of the distribution of repair costs. Find an interval within which these weekly repair costs should lie at least 75% of the time using Tchebysheff's Theorem. Find an interval within which these weekly repair costs lie exactly 75% of the time with exactly half of those not lying in the interval above the upper limit and the other half below the lower limit. Compare this interval to the one obtained in part (b). 5.16 In a genetics study, it was found that the distance X between mutations in a certain strand of DNA had a probability density function given by te-x/5, x > 0 f (x) : 0, otherwise with measurements in kb. a Find the mean and variance of the distribution of distances between mutations in this strand of DNA. Find an interval within which these distances between mutations should lie at least 75% of the time using Tchebysheff's Theorem. Find an interval within which these distances between mutations lie exactly 75% of the time with exactly half of those not lying in the interval above the upper limit and the other half lying below the lower limit. Compare this interval to the one obtained in part (b).
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