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tutorial04

# tutorial04 - ISMT 111 BUSINESS STATISTICS TUTORIAL 4...

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1 ISMT 111 B USINESS S TATISTICS T UTORIAL 4 created by Andrew Yam Continuous Random Variable § Suppose X is a continuous r.v., then ( 29 0 = = x X P for < < - x . § ( 29 b X a P is the area under the curve of probability density function (p.d.f.) within the interval (a, b) . § ( 29 1 = < < - X P § Note: For continuous r.v., ( 29 ( 29 ( 29 1 0 2 = + = < X P X P X P Uniform Distribution § X is a uniform random variable and we denote it as X ~ U(a, b) § The p.d.f. of X : ( 29 a b x p - = 1 if a < x < b; or ( 29 0 = x p otherwise § Mean: ( 29 2 b a X E + = = m § Variance: ( 29 ( 29 12 2 2 a b X Var - = = s Normal Distribution § X is a normal random variable and we denote it as X ~ N( m , s 2 ) , where m and s 2 are the mean and variance of X respectively. § Bell-shaped curve symmetric at the mean m § The p.d.f. of X : ( 29 ( 29 - - = 2 2 2 2 exp 2 1 s m ps x x p §

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2 § Every normal random variable
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tutorial04 - ISMT 111 BUSINESS STATISTICS TUTORIAL 4...

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