BIOL 570 1nd Edition Lecture 5 Outline of Last Lecture I. Estimationa. Point estimationII. Errora. Sampling errorIII. Sampling distributionIV. Standard error a. Definitionb. calculationV. 95% confidence interval a. Definitionsb. Calculation using the 2SE rulec. interpretationOutline of Current Lecture I. Review of chapter 4II. ProbabilityIII. Definitions: random trial, sample space, event, probability, mutual exclusive eventsIV. Probability Rules 1-5 Current LectureChapter 4 Reviews2 > s > SEῩ (variance > standard deviation > standard error of mean) frequency 95% Ῡ-µ = errorῩ 95%CI µ centered Ῡ ± 2 SEῩThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Chapter 5-General recipe for solving probability problems (printout)-Random trial- an experiment that could be repeated with differing outcomesSamples space- the set of all possible outcomes of a random trialEx. dice S= {1,2,3,4,5,6}Event- a possible result of a trial. Can be any subset of the sample spaceR is a roll, R=1Rule #10 ≤ P(Ei) ≤ 10 means impossible1 means guaranteed *cannot be negativeTwo events are mutually exclusive if they couldn’t occur on the same trial. Rule #2If a set(s) of mutually exclusive events and covers the entire sample then: ƩP(Ei) = 1What is the probability of rolling a 2 on a fair 6-sided die?P(r=2) = 1/6P(r=1) = P(r=2) = P(r=3) = P(r=4) = P(r=5) = P(r=6)ƩP(E) = 1A population has an equal number of males and females. Brown, black and blond hair colors areequally frequent in the population. S= {M, F, brown, black, blond}SG= {M, F}P(M) = P(F)Ʃi P(E) = 1 = ½ + ½ Rule #3If events A and B are mutually exclusive then: P(A or B) = P(A) + P(B)“or” = ADDWhat is the probability of rolling an odd number?P(odd) = P(1 or 3 or 5)= P(1) + P(3) + P(5)= 1/6 + 1/6 + 1/6 = ½ What is the probability that the roll would be something other than 5?P(r≠5) = P(not (r= 5))Complement ruleP(not A) = 1 - P(A)P(A) + P(not A) =11 – P(r=5)1 - 1/6 = 5/6What is the probability that a roll will be odd or less than 4?P(r<4 OR r is odd)P(r<4) + P(r is odd) WRONG!!!= ½ + ½ = 1r<4 is not mutually exclusive of r is oddRule #5General additionP(A or B) = P(A) + P(B) – P(A and B)* P(A,B) – joint probabilityP(r is odd and r<4)= 2/6P(r<4 or odd) = 3/6 + 3/6 – 2/6 =