2. The Central limit Theorem The central limit theorem (CLT)ifX,X2,., Xn is a random sample from any population(i.e, probability distribution)with mean u and variance o2. the sample mean tends to be normally distributed with mean u and variances/ as the sample size increases indefinitely (technically, infinitely.) The sample mean of a sample drawn from a normal population follows the normal distribution regardless of the sample size. Uniform distribution the pdF of a continuous rv. x on the interval from a to b 1)The PDF f=、1 <X<b 0 otherwise 2)Mean and variance b ECX) var(X) (b-a) 122. The Central Limit Theorem The central limit theorem (CLT)—if X1 ,X2 , ..., Xn is a random sample from any population (i.e., probability distribution) with mean μ and variance σ2 , the sample mean tends to be normally distributed with mean μ and varianceσ2 /n as the sample size increases indefinitely (technically, infinitely.) The sample mean of a sample drawn from a normal population follows the normal distribution regardless of the sample size. Uniform distribution:the PDF of a continuous r.v. X on the interval from a to b. 1) The PDF 2) Mean and variance 0 otherwise 1 ( ) =   − = a X b b a f X 12 ( ) var( ) 2 E(X) 2 b a X a b − = + =