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Title: Probability distributions
Description: This file is a pdf for the topic "probability distributions" from the subject " probability and statistics"

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Lecture Notes

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Prepared by

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15MA301-Probability & Statistics

Dr
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ATHITHAN

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Assistant Professor

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Department of Mathematics
Faculty of Engineering and Technology
SRM INSTITUTE OF SCIENCE AND TECHNOLOGY

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Kattankulathur-603203, Kancheepuram District
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Probability & Statistics

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1 Binomial Distribution
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2 Mean and Variance of Binomial Distribution
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2 Poisson Distribution
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2 Mean and Variance of Poisson Distribution
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3 Geometric Distribution
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2 Mean and Variance of Geometric Distribution
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Standard Continuous Distributions
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1 Moment Generating Function of U NIFORM D ISTRIBUTION
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1 Moment Generating Function of E XPONENTIAL D ISTRIBUTION
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2 Mean and Variance of Exponential Distribution
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1 MGF of Normal Distribution
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Example Worked out Problems

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Exercise/Practice/Assignment Problems


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Probability & Statistics
Unit-2

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? Functions of Random Variables

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Probability & Statistics

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Standard Discrete Distributions
Binomial Distribution

The Probability Mass Function (P
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Note that

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Second Moment = E(X 2 ) = MX00 (0)
MX00 (t) = np[et (q + pet )n−1 + et (n − 1)(q + pet )n−2 pet ]
MX00 (0) = np[1 + (n − 1)p] = np + n2 p2 − np2

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Var(X) = E(X 2 ) − [E(X)]2
= np + n2 p2 − np2 − n2 p2 = np − np2
= np(1 − p) = npq

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Poisson Distribution

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P (X = x) =

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The Probability Mass Function (P
Title: Probability distributions
Description: This file is a pdf for the topic "probability distributions" from the subject " probability and statistics"