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1. STAT 114Probability&Statistics
Week-5 Lecture-9
Semester- Fall 2018
Prepared by:
MR ARSHAD HAMEED
Lecturer
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2. Course Content
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3. Preamble (Past Lesson Brief)
 Basic Discrete random Variable and Probability distribution
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4. Continuous Random Variables
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5. Properties Continuous Random
Variables
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6. Mean and Variance of continuous
random variable
 The expectation of a continuous random variable X with probability density
function f is the number
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



 x
x
xf
X d
)
(
]
[
E
2
2
]
[
E
]
[
E
)
(
Var X
X
X 


7. Questions
Q:1 A random variable X is of continuous type with p.d.f.
f(x)=2x, 0<x<1,
=0, elsewhere
 Find its mean and variance
Q:2 Find the mean and Variance of the random variable X having the p.d.f
f(x)=2(1-x) , 0<x<1
=0, elsewhere
Find its mean and variance
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8. HOME ASSIGNMENT
Q:3 A random variable X has a density function given by
f(x)=4(𝑥 − 𝑥3
) 0<x<1,
=0, elsewhere
 Find its mean and variance
Q:4 Given the following function
f(x)=
2
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(4𝑥 − 2𝑥3) 0<x<2
=0, elsewhere
compute its mean .
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9. HOME ASSIGNMENT
Q:5 A random variable X has a density function given by
f(x)=𝑥3
(1 − 𝑥 ) 0<x<1,
=0, elsewhere
Q:6 Given the following function
f(x)=
3
4
𝑥(2 − 𝑥) 0≤x ≤ 2
=0, elsewhere
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10. Q & A
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11. References
 Probability and Statistics for Engineers and Scientists by Ronald E.
Walpole, Raymond H. Myers, Sharon L. Myers and Keying E. Ye, Pearson;
9th Edition (January 6, 2011). ISBN-10: 0321629116 2
 Walpole, P.E., Myers R.H., Myers S.L. (1998), “Probability and Statistics for
Engineers and Scientists”, 7th Ed. Prentice Hall.
 Introduction to Statistical Theory Part 1,Prof Sher Muhammad Chaudhry
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