100Bnote1

100Bnote1 - STAT 100B Note for Midterm Note: Please try to...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STAT 100B Note for Midterm Note: Please try to understand the logic flow, instead of just memorizing the formulas. 1 Topics (1) Point estimate: bias and variance. (2) Hypothesis testing: null hypothesis, alternative hypothesis, test statistic, reference distribution, p-value, decision rule, type I error, type II error. (3) Confidence interval. (4) Inference of population proportion (or probability) (5) Inference of population average (or expectation). (6) Linear regression, best linear unbiased estimator, least squares principle. 2 Probability preparation (1) For a random variable X , E( aX + b ) = a E( X )+ b , Var( aX + b ) = a 2 Var( X ), where a and b are two constants. (2) For a sequence of random variables, X 1 , X 2 , ..., X n , E( n i =1 X i ) = n i =1 E( X i ). If these random variables are independent, then Var( n i =1 X i ) = n i =1 Var( X i ). (3) We can apply (1) and (2) together. For instance, if E( X i ) = and Var( X i ) = 2 , for i = 1 ,...,n , then E( X ) = and Var( X ) = 2 /n . (4) Normal distribution. If a random variable X N ( , 2 ), then Z = ( X- ) / N (0 , 1), and the statement X ( a,b ) is equivalent to Z ( a ,b ), where a = ( a- ) / , and b = ( b- ) / , so Pr( X ( a,b )) = Pr( Z ( a ,b )). We can look up the normal table to get Pr( Z ( a ,b )). 3 Inference of population proportion or probability The data and the model: X 1 ,X 2 ,...,X n are independent binary random variables from Bernoulli( p ). Example 1: p is the probability of getting a head in coin flipping. X i = 1 if the i-th flip is a head, and X i = 0 otherwise. Example 2: p is the population proportion of those who are going to vote for a candidate. X i = 1 if the i-th person in the random sample says that he or she is going to vote for this candidate, and X i = 0 otherwise....
View Full Document

Page1 / 3

100Bnote1 - STAT 100B Note for Midterm Note: Please try to...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online