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# Fall 2016 (Total Marks 15)

Your Assignment must be uploaded/ submitted before or on 19th January, 2017

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 this Assignment:

• This assignment will strengthen the basic idea about the concept of the following topics:
• Mathematical Expectation, Variance and Moments of a continuous probability distributions
• Bivariate probability distribution (Discrete and Continuous)
• Properties of Expected values in the case of Bivarite probability distribution
• Some well known Discrete probability distributions

Assignment.2 (Lessons 24-27)

Question:                                                                                Marks: 5++5+5=15

A joint function of (X,Y)  is given by the following equation:

(a)   Show that given fulfills the conditions of a p.d.f.

(b)   Compute the Marginal Probability density function of variable X

(c)   Calculate the Expected value of X i.e, E(X).

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### Replies to This Discussion

plz giv eme accurate soution thanks

Just an idea solution

is it correct or not related to the assignment

how it solved in last three lines and middle line?

Need assistance please or share ideas

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&

Koe word pa bana ka send kar da plz

Asa, Plz can anyone tell from where i may get the math type software?

yes u can find the application in vu lms download section mathtype 6.9 full rar etc ye name likha ho ga to wahan se download ker k install ker len us k sath key b ho g
agr smj na aye to puch lena

download section k second page pe likha he ye MathType 6 full.rar
es pe click ker k download ker lo ok he gor se dekho

Q1)   A joint function of (X,Y)  is given by the following equation:

(a)   Show that given fulfills the conditions of a p.d.f.

(b)  Compute the Marginal Probability density function of variable X

(c)   Calculate the Expected value of X i.e, E(X).

Solution a :

4xy2 / 3  +4xy2 )dydx =1

(4xy /6  + 4xy3 /3 )1 dx =1

(2xy /3 + 4xy3 /3 )1 dx =1

{2x / 3 [ (1) - (0)2] +4x/3 [(1)3 – (0)3  ]}  dx =1

(2x/ 3 + 4x/3) dx =1

( 2/3 (x2 /2) + 4/3 (x2 /2))1 =1

(x / 3 + 2/3x2)1 = 1

1/ 3 [ (1)2 –(0)2] + 2/3[ (1)2+(0)2] =1

by simplifying

3/3 =1

1=1   Hence F(x,y) is p.d.f

(b)      g(x)  =f(x,y)dy

4xy(1/3+y)dy

(4xy/3+4xy2)dy

Opening integration

[4 x/ 3  (y2 / 2) + 4x (y3 / 3)]10

2x/3[(1) - (0)2] + 4x / 3 [(1)3 – (0)3]

g(x) =  2x / 3 + 4x/3  marginal probability of x

(c)   E(x) = xg(x)dy

2x/3+ 4x / 3 )dx

2x2/3+ 4x 2/ 3 )dx

[2/3 (x3/3)+ 4/3 (x3 /3)]10

simplifying

2 /9 [(1)3 – (0)3]  + 4/9 [(1) - (0)3]

2 / 9 + 4 / 9

6 / 9

E (x) = 2 /3

sorry for maths type

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