topic03a

# topic03a - x 1,x 2 …… x n-1 x n The probabilities...

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Topic 3 Discrete Probability Distributions Part A 3.1 A random variable is a numerical description of the outcome of an experiment. A random variable can be classified as being either discrete or continuous depending on the numerical values it assumes. A discrete random variable may assume either a finite number of values or an infinite sequence of values. A continuous random variable may assume any numerical value in an interval or collection of intervals. 3.2 Main features of a discrete probability distribution are: The sum of the probabilities of the various outcomes is 1.00. The probability of a particular outcome is between 0 and 1.00. The outcomes are mutually exclusive. 3.2 Expectation : In general , there are n different possible values for random variable X:
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Unformatted text preview: x 1 ,x 2 , …… x n-1 , x n . The probabilities correspondingly are p 1 ,p 2 …… p n-1 , p n where p i =P(X= x i ) then the mean of X or the expection of X can be calculated as 3.3 Variance 3.4 Covariance : 3.5 Properties of Expectation : 3.6 Properties of Variance: n n n n n i i i p x p x p x p x p x X E + + + = = = − − = ∑ 1 1 2 2 1 1 1 ... ) ( μ 2 2 2 1 2 2 [E(X)]-) E(X ] ) [( ) ( ) ( = − = − = = ∑ = σ X E p x X Var n i i i b X E b X E X aE aX E Y E X E Y X E + = + = + = + ) ( ) ( ) ( ) ( ) ( ) ( ) ( t independen Y X, only when ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 Y Var X Var Y X Var X Var b X Var X Var a aX Var + = + = + = )] , ( ) )( [( i i Y i X i i XY y x P y x − − Σ =...
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