Stat 425 Lecture1

STAT 420 Examples for 01/1 5/2013 spnng 2013 Bivariate Normal Distribution: f(x,y)¯ I-p2 2 TIOI 02 o ox-plo 021 exp 2 10 -p2 ox-pl -2P0 Y -p 2 ooy -p 20 0+0 0200020 the marginal distributions of X and Y are N p 1 , 01 0 and NO p respectively; the correlation coefficient of X and Y is independent if and only if 02 20 01 -p2)020; the conditional distribution of X, given Y = Y, is the conditional distribution of Y, given X = x, is p p, and X and Y are p2)0120. X + b Y is normally distributed with mean E(aX+ +b variance and +2abp01 02+b202. p 03 p 06 p 09 A large class took two exams. Suppose the exam scores X (Exam 1) and Y (Exam 2) follow a bivariate normal distribution with p 1=70, p 2=60, 01=10, 02=15, p = 0. 6. a) A students is selected at random. What is the probability that his/her score on Exam 2 over 75? b) Suppose you''re told that a student got a 80 on Exam 1.

What is the probability that ) Suppose you''re told that a student got a 66 on Exam 1. What is the probability that his/her score on Exam 2 is over 75? d) Suppose you''re told that a student got a 70 on Exam 2. What is the probability that his/her score on Exam 1 is over 80? A students is selected at random. What is the probability that the sum of his/her Exam 1 and Exam 2 scores is over 150? f) What proportion of students did better on Exam 1 than on Exam 2?