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Lecture 06-continuous probability distributions

# Lecture 06-continuous probability distributions - 1036...

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Prob. & Stat. Lecture06 - continuous probability distribution 6-1 1036: Probability & Statistics 1036: Probability & 1036: Probability & Statistics Statistics Lecture 6 Lecture 6 Some Continuous Some Continuous Probability Distributions Probability Distributions

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Prob. & Stat. Lecture06 - continuous probability distribution 6-2 Continuous Uniform Distribution A flat density function defined on a closed interval. The density function of continuous uniform random variable X on the interval [ A , B ] is elsewhere , 0 , 1 ) , ; ( B x A A B B A x f = Mean: Variance: ( ) 2 B A + = µ ( ) 12 2 2 A B = σ Constant weight Proof.
Prob. & Stat. Lecture06 - continuous probability distribution 6-3 Normal (Gaussian) Distribution The density function of the normal random variable X , with mean µ & variance σ 2 , is ( ) . , 2 exp 2 1 ) , ; ( 2 2 < < = x x x n σ µ π σ σ µ A function depends on µ and σ Mean: µ Variance: σ 2 Proof.

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Prob. & Stat. Lecture06 - continuous probability distribution 6-4 Remarks Normal curve is dependent on the mean and standard deviation