321 Stat Day 4
Probability (2.1)
Reminders
Lab 2 due Friday
Will discuss similar issues in lecture Ask questions in class/office hours/email Can download data from web
HW 1 due Tuesday
Ch. 1 questions?
Example 3: More Matching
1 2
3
4
5
Heights Number of siblings Last haircut cost Change in pockets Guesses of my age
Excel?
Column1 Mean Standard Error Median Mode 22.20533 1.213832 20.855 #N/A
Histogram
14
12 10 Frequency 8
Standard Deviation
6.648431
44.20163 5.085073 1.85294
Sample Variance
Kurtosis Skewness
Range
Frequency
32.75
13.71 46.46 666.16
6
4 2 0
Minimum Maximum Sum
Count
13.71 20.26 26.81 Bin 33.36 39.91 More
30
Example 1: Monty Hall Problem
Definition: Probability
We will consider the probability of an outcome to be the long-run proportion (relative frequency) of times the outcome occurs if the experiment is repeated over and over under identical conditions. Determining probabilities
Simulation Exact analysis...
Assigning Probabilities
Two rules:
For any event A, P(A) > 0 P(S) = 1 Thus, 0 < P(A) < 1 for any event A
Solution to Monty Hall Problem
Reveal Door 1 pig, $, pig 0 Reveal Door 2 Reveal Door 3 150 Total 300
150 0
300
pig, $, pig pig, pig, $
Total
0
0
300
0
300
300 900
P(win if staying) = 300/900
P(win if switching) = 600/900
Example 2: Grad School Admissions
Suppose that you have applied to two graduate schools, A and B. You believe that the probability of getting accepted by A is .8, by B is .4, and the probability of being rejected by at least one is .65. (a) What is the probability of getting accepted by at least one of the schools?
Example 2: Grad School Admissions
Accepted by A Denied by A Total
Accepted by B Denied by B
Total
Example 2: Grad School Admissions
Accepted by A Denied by A Total
Accepted by B Denied by B
Total 800 200
400 600
1000
Example 2: Grad School Admissions
Accepted by A Denied by A Total
Accepted by B Denied by B
Total
350
400 600
800
200
1000
Example 2: Grad School Admissions
Accepted by A Denied by A Total
Accepted by B Denied by B
Total
350 450
800
50 150
200
400 600
1000
P(accepted by A or B (or both)) = 850/1000 = .85
P(A B) vs. P(A' B')
A A
B B
For Tuesday
HW 1 due Continue with Lab 2
Any questions so far?