1. The distribution of the amount of gravel (in tons) sold by a particular construction supplycompany in a given week is having random variable X with commulative distribution (cdf)function F is defined below0,x < 00 < x <1F(x) = { (a + 23)(x² + 1),*+ 16 2< x < 5/2x > 5/24ax,1< x < 21,Using the property of F(a) = F(a+) = lima+ F(x), find the value of a, ß for which F(.)is a cdf function.

Answered: 1. The distribution of the amount of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)
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1. The distribution of the amount of gravel (in tons) sold by a particular construction supply company in a given week is having random variable X with commulative distribution (cdf) function F is defined below 0, x <0 0 < x <1 (a + 23)(x² + 1), + t 2< x < 5/2 x 2 5/2 4ax, F(x) = 1