DISCRETE RANDOM VARIABLE

PRESENTED BY MOHAMMAD ABDULLAH AL MAYIN ID:152-33-2629 (EEE 213)

CONTENTS

I. Discrete random variableII. Classification of discrete random variable:

III. Probability mass functionIV. Cumulative distRibution function

V. Expectation ,variance & standerd daviation of drv

A discrete random variable: has a countable number has a finite value.

NOW COUNT THE NUMBER OF GIRLS IN EACH SET OF FOUR SEQUENTIAL BIRTHS:

BBBB (0) BGBB (1) GBBB (1) GGBB (2)BBBG (1) BGBG (2) GBBG (2) GGBG (3)BBGB (1) BGGB (2) GBGB (2) GGGB (3)BBGG (2) BGGG (3) GBGG (3) GGGG

BBBBBGBBGBBBBBBGBBGBGGBBGBBGBGBGBGGBGBGBBBGGBGGGGBGGGGGBGGBGGGGG

0

1

2

3

4

X

Sample Space

DISCRETE RANDOM VARIABLE(CONT.)

PROBABILITY MASS FUNCTION

xiall

iPKXPKF )()()(

The cumulative distribution function, F(x), of a discrete random variable X is:

CUMULATIVE DISTRIBUTION FUNCTION

FIG 1

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1.Sum of probability of each value of the random variable2.After average all probability

E X xP xall x

( ) ( )

x P(x) xP(x)0 0.1 0.01 0.2 0.22 0.3 0.63 0.2 0.64 0.1 0.45 0.1 0.5 1.0 2.3 = E(X) = m

EXPECTED VALUES OF DISCRETE RANDOM VARIABLES

• FIG 2

The variance of a random variable is the expected squared deviation from the mean:

The standard deviation of a random variable is the square root of its variance: )()( XVXSD

VARIANCE AND STANDARD DEVIATION OF A RANDOM VARIABLE

CONCLUSION In bottom line I want to say:

Random variable is major factor in engineering.Discrete random variable is

a part of random variable.So it’s importance is very high.We can learn it perfectly.

THANKS EVERYONE