Probability Density Function-Probability-Assignment Solution, Exercises of Probability and Statistics

Probability course is not being taught in mathematics but its important in engineering, physics, computer science etc. Every science field. This is solved assignment for Probability. It includes: Probability, Destiny, Function, Statistical, Notations, Calculus, Integrate, Margin, Distribution

Typology: Exercises

2011/2012

Uploaded on 08/03/2012

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Assignment No.3 (Course STA301)
Spring 2012 (Total Marks 15)
INSTRUCTIONS
Deadline:
Your Assignment must be uploaded/ submitted before or on
23:59 13th, 2012
STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR
ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE
DATE WILL BE ACCEPTED VIA E.MAIL.
Rules for Marking:
It should be clear that your Assignment will not get any credit IF:
The Assignment submitted, via email, after due date.
The submitted Assignment is not found as MS Word document file.
There will be unnecessary, extra or irrelevant material.
The Statistical notations/symbols are not well-written i.e., without using
MathType software.
The Assignment will be copied from handouts, internet or from any other
student’s file. Copied material (from handouts, any book or by any website)
will be awarded ZERO MARKS. It is PLAGIARISM and an Academic
Crime.
The medium of the course is English. Assignment in Urdu or Roman
languages will not be accepted.
Assignment means Comprehensive yet precise accurate details about the
given topic quoting different sources (books/articles/websites etc.). Do not
rely only on handouts. You can take data/information from different
authentic sources (like books, magazines, website etc) BUT express/organize
all the collected material in YOUR OWN WORDS. Only then you will get
good marks.
Objective(s) of the Assignment:
The current assignment will help out students for:
Understanding about the application of probability distributions.
Establishing the link between discrete probability distribution and
continuous probability distribution.
Getting hands-on practice to find out the joint probability distribution.
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Assignment No.3 (Course STA301)

Spring 2012 (Total Marks 15)

INSTRUCTIONS

Deadline:

Your Assignment must be uploaded/ submitted before or on

th

STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR

ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE
DATE WILL BE ACCEPTED VIA E.MAIL.

Rules for Marking:

It should be clear that your Assignment will not get any credit IF:The Assignment submitted, via email, after due date.The submitted Assignment is not found as MS Word document file.There will be unnecessary, extra or irrelevant material.The Statistical notations/symbols are not well-written i.e., without using MathType software.The Assignment will be copied from handouts, internet or from any other student’s file. Copied material (from handouts, any book or by any website) will be awarded ZERO MARKS. It is PLAGIARISM and an Academic Crime.The medium of the course is English. Assignment in Urdu or Roman languages will not be accepted.Assignment means Comprehensive yet precise accurate details about the given topic quoting different sources (books/articles/websites etc.). Do not rely only on handouts. You can take data/information from different authentic sources (like books, magazines, website etc) BUT express/organize all the collected material in YOUR OWN WORDS. Only then you will get good marks.

Objective(s) of the Assignment:

The current assignment will help out students for:

Understanding about the application of probability distributions.Establishing the link between discrete probability distribution and continuous probability distribution.Getting hands-on practice to find out the joint probability distribution.

Assignment No: 3 (Lessons 23-30)

Question 1: Marks: 5 +

The probability density function of a random variable is given

f(x) = 2(x-1) 1<x < 2 0 Elsewhere Calculate second moment about origin.

Sol

2 2

2 2

2 2 2 1 2 3 2 1 2 2 3 2 1 1 4 2 32

1 1 4 4 3 3

E x x f x dx

E x x x dx

E x x x dx

x x dx

x dx x dx

x x

 



 ^ ^ 

b) Let x and y are two independent r.v.’s with joint probability density function.

Find the marginal probability density function g(x).

Sol

x 1 3 y

f(x,y)

^2

 0 < x < 2, 0 < y < 1

= 0, elsewhere.

We will use the continuity correction for finding the required probability. The interval at least 25 indicates 25; therefore it starts at 24.5 to infinity by continuity correction

X 1/ 2 Z

Z
P ( 1.1   Z   ) P ( 1.1   Z  0)  P (0  Z  )

By using area table, we can easily find = 0.3643 + 0.5 = 0.