Answered: f (x) = c/x3 for 1 < x < ∞; Find the…

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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Question

f (x) = c/x3 for 1 < x < ∞; Find the constant c so that f (x) is a
pdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphs
of the pdf f (x) and the cdf F (x), and find the mean μ and variance σ².

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

Expert Solution

Step 1: Given information

Given the function

$f left parenthesis x right parenthesis space equals open curly brackets table row cell fraction numerator c over denominator x cubed space end fraction space space space space space space space semicolon space 1 less than x less than infinity end cell row cell 0 space space space space space space space space space space space space semicolon space o t h e r w i s e end cell end table close$

want to find the value of c such that the given function will be pdf.

also wants to find CDF. Plotting of PDF and CDF and mean and varaince.