20. A continuous random variable X has CDF given byif x <1F(x) =2(x - 2 + 1/x) if 1

As Prof. A. K. Giri defined, "Probability Density Function: A continuous function f(x) is said to be…

Answered: 20. A continuous random variable X has…

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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a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum of the two results. Calculate E[X2]. (b) Suppose that X has pdf given by f(x) = 3x^(−4) if x > 1 and by f(x) = 0 if x <= 1. Calculate the median of X.
6) Allow a continuous probability distribution to be defined as f(x) = 4x³ for the range 0 sxs1. Demonstrate that the area underneath the curve is 1 (the function integrates to 1) and calculate the mean and variance of the probability distribution.
Find the method of moments estimator for the parameters of the double exponential distribution DE(0,n) f(x) Le-lz-nl/, - 0 0. 20
Let X₁,..., Xn be an iid random sample from a Uniform(0, 0), where 0 > 0. Let X(n) = max{X₁, (a) Find the mean and variance of X(n). (b) Find the limiting distribution of Zn = n (0 – X (n)). (c) Find the limiting distribution of log(Zn). Xn}
4
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
and variance of X if the probability mass function is f(x) = ; ;)" , Find the moment generating function, mean x = 1, 2, 3, 4, ...
The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…
A continuous random variable X is defined by f ( x ) = (3+x)^2/16 ; -3<x<-1 f(x) = = ( 6 - 2x^2)/16 ; -1<x<1 f(x) = ( 3 - x^2)/16 ; -1<x<3 a. Verify that f(x) is density b. find the mean
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 '3 - x²) 0sx <1 f(x) =2 %3D elsewhere Find the expected value and standard deviation of the amount of gravel sold in a week, a) 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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20. A continuous random variable X has CDF given by if x <1 F(x) ={2(x – 2 + 1/x) if 1