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