The daily consumption of natural gas in liters of a particular building is a randomvariable x with probability density function X1≤x≤2k(1-1/2)f(x) =- { *(0elsewherea) calculates the appropriate value of K so that the distribution is probabilisticdensityb) calculate the expected valuec) calculate the standard deviation

Given: The random variable X with probability density function, fx=k1-1x2 1≤x≤20…

Answered: The daily consumption of natural gas in…

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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Two random variables X and Y with a joint PDF f(x,y) = Bx+y for 0≤ x ≤6 , 0≤ x ≤7 and constant B Find value of constant B
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Let X ~ Uniform(a, b). Find Expected value EX.
Let the weights of 1 kg tea boxes filled with an automatic machine have a normal distribution with a mean of μ=1.03 and a standard deviation of σ=0.02 kg.a) What is the probability that any tea box will weigh less than 1 kg?b) What is the probability that any tea box will weigh higher than 1,06 kg?
The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630
the probability density function for the waiting time was given by f(x) = 0 for x 15 a) Find the expected value of the waiting time, X minutes. b) Find the variance and standard deviation of the waiting time. c) What is the probability that the waiting time is within two standard devia- tions of its expected mean value? 1 15
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Write a function mysquares[v, m, μ, o] that constructs m samples of v sums-of-squares of the deviation from the mean (as in the workbook) with the X; drawn from the normal distribution N(μ, o). Also write histxsq[v, m, µ, σ] to plot a PDF histogram of your samples (with Automatic bspec), with the appropriate x² PDF plotted over the top. With m = 10 000, plot a few examples to see how well the x² distribution fits your samples. [Say v= 2, µ = 1, σ=2; v = 6, μ = 3, 0 = 10; v = 16, μ = 0, 0 = 1.]
The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular construction supply company in a given week is a continuous random variable X with PDF as f(x)={█(3/2 〖(1-x〗^2) 0≤x ≤1@0 elsewhere)┤ Find the expected value and standard deviation of the amount of gravel sold in a week. Consider a normally distributed random variable X with a mean of 85 and standard deviation of 10. Find P(90≤X≤100)?
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