Problem 1 In probability theory, a random variable X is a function from sample space of a random experiment (the set of all possible outcomesi to the real numbers. For instonce, if we were to choose a person ot random, we might let X= height of selected person. We might ask What is the probability that the selected person is between 18 and 19 meters tal? with the symbols P(18

Problem 1 In probability theory, a random variable X is a function from sample space of a random experiment (the set of all possible outcomesi to the real numbers. For instonce, if we were to choose a person ot random, we might let X= height of selected person. We might ask What is the probability that the selected person is between 18 and 19 meters tal? with the symbols P(18

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Sorry Accidentally uploaded wrong image for problem 1

Problem 1
In probability theory, a random variable X is a function from sample space of a random experiment
(the set of all possible outcomesi to the real numbers. For instonce, if we were to choose a person ot
random, we might let X= height of selected person. We might ask What is the probability that the
selected person is between 18 and 19 meters tal? with the symbols P(18<X<19). To answer
this question often requires calculus
The probabilities for certain random variables ore determined by the area under a curve related to
the random variable, colled the probability density function. Iff(x)is the probability density function
for the variable X then P(18 <X <1.9) - rdr.
A condition on anyprobability density function is that f(x)dx = 1.0ne of the most common
types of continuous random variables is a normal random variable, which has the probability density
function
f(x) =
-e-(x-w)²/(2a ²),
The constants u and a are the mean and the standard deviation of the distribution. If we know these
values, we can compute all probabilities related to this graph. The density curve has the familiar bel-
shaped graph.
Using multivariable colculus it can be shown that
e-(x-H)*/(20 ²)dx = 1.
Lo t-f(x)dx =
Recall the moment about the y -axis. In probability theory the first) moment has the interpretation of
giving the mean of a random variable. Your tosk is to confirm this for the normal random variable

Take a- land this reduces to showing that
xe-(x-w)³/(2)dx = µ.
V2n
Begin with the substitution u =x-u. This allows you to seporate this into two separate
integrals.
• One integral is a constant times
V2
which was given
• The other Integral can now be computed with another substitution and our method for
computing improper integrals.

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