The time, X, for clearing side effects of water purification, in days, has the following cumulative distribution F: F(x) = 0 for x < 1 and F(x)= VX - for 1 s x s 9 and F(x) = 1 for x > 9 2 a) What is the probability density function for X for 1 s x s 9? f(x) o f(x) 2 O (x) 1. O F(x) 4x %3D O f(x) = .125 b) What is the probability that X > 5? c) What is the probability X < 5 ? d) What is the probability that X > 7? e) What is the probability that X > 6.3? f) What is the probability that X > 7 given the X > 6.3? g) Calculate the 70th percentile of x. h) What is the expected value of X? i) What is the expected value of x2 ? j) What is the variance of X? k) What is the probability that X is more than 0.1 below its expected value?

The time, X, for clearing side effects of water purification, in days, has the following cumulative distribution F: F(x) = 0 for x < 1 and F(x)= VX - for 1 s x s 9 and F(x) = 1 for x > 9 2 a) What is the probability density function for X for 1 s x s 9? f(x) o f(x) 2 O (x) 1. O F(x) 4x %3D O f(x) = .125 b) What is the probability that X > 5? c) What is the probability X < 5 ? d) What is the probability that X > 7? e) What is the probability that X > 6.3? f) What is the probability that X > 7 given the X > 6.3? g) Calculate the 70th percentile of x. h) What is the expected value of X? i) What is the expected value of x2 ? j) What is the variance of X? k) What is the probability that X is more than 0.1 below its expected value?

Name: The time, $ X $, for clearing side effects of water purification, i
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Description: The time, $ X $, for clearing side effects of water purification, in days, has the following cumulative distribution $ F $:- $ F(x) = 0 $ for $ x < 1 $ - $ F(x) = \frac{\sqrt{x}}{2} - \frac{1}{2} $ for $ 1 \leq x \leq 9 $- $ F(x) = 1 $

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

The time, $ X $, for clearing side effects of water purification, in days, has the following cumulative distribution $ F $:

- $ F(x) = 0 $ for $ x < 1 $
- $ F(x) = \frac{\sqrt{x}}{2} - \frac{1}{2} $ for $ 1 \leq x \leq 9 $
- $ F(x) = 1 $ for $ x > 9 $

### Questions:

a) What is the probability density function for $ X $ for $ 1 \leq x \leq 9 $?

- $ f(x) = \frac{1}{4\sqrt{x}} $
- $ f(x) = \frac{\sqrt{x}}{2} $
- $ f(x) = \frac{\sqrt{x}}{2} - \frac{1}{4} $
- $ f(x) = \frac{1}{4x} $
- $ f(x) = .125 $

b) What is the probability that $ X > 5 $?
[__________]

c) What is the probability $ X < 5 $?
[__________]

d) What is the probability that $ X > 7 $?
[__________]

e) What is the probability that $ X > 6.3 $?
[__________]

f) What is the probability that $ X > 7 $ given $ X > 6.3 $?
[__________]

g) Calculate the 70th percentile of $ X $.
[__________]

h) What is the expected value of $ X $?
[__________]

i) What is the expected value of $ X^2 $?
[__________]

j) What is the variance of $ X $?
[__________]

k) What is the probability that $ X $ is more than 0.1 below its expected value?
[__________]

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