Edpsy 590 Lab (2)
Feb. 6, 2006
Exercises for Homework 2
Question 2 - Probability
Study point – “conditional probability”
A. Similar problem
A sociologist identified 270 distinct neighborhoods in a large American city. The number of neighborhoods in
each combination of classifications is shown in the following table.
Income
Ethnicity Balance
Low
Medium
High
Minority
79
9
3
Mixed
22
20
10
Nonminority
18
63
46
Q. Determine the conditional probability that it will have the characteristics of
(a) Low income, given that it is minority
(b) High income, given that it is minority
(c) Nonminority, given high income
(d) Medium income, given mixed
(e) Not medium income, given mixed
Question 3 – probability
Study point – “ Bayes’s Theorem”
P (A l B) = P (B l A) * P (A) / P (B)
Bayes’s theorem gives a way to find the conditional probability of event A given event B, provided that you
know that probability of (A), probability of (B), and the conditional probability of B given A. Bayes’s Theorem
is often used to calculate a new conditional probability when some initial probabilities are known. For this
reason, it is called “posterior probability.”
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Edpsy 590 Lab (2)
Feb. 6, 2006
Exercises for Homework 2
The simplest case is as follows. We have a hypothesis, H. For example, H = "This new power supply is
defective.". There is clearly some uncertainty in this statement. The question is, how much? A second question is,
how would you quantify the uncertainty?
Call the probability of H, p(H). That is, p(H) is the probability that a randomly chosen new power supply is
defective. To determine a value of p(H) someone would have to thoroughly test a large sample of power supplies.
Presumably that is just what the manufacturer's quality control people do.
Now suppose you have a subset of these new power supplies, those with noisier fans. Suppose E= "the new
power supply has a noisy fan".
Now we ask, what is the probability that the new power supply is defective, given that the fan is noisy? This
probability is written, p(H | E), the probability of H occurring, given E has occurred. (Intuitively we would be
worried that p(H | E) > p(H).) We can think of E as evidence that the power supply is defective.
Often p(H | E) is not so easy to measure. Bayes found a simple formula which "turns p(H | E) around". The
formula is,
p(H | E) = p(E | H) *p(H) / p(E)
Here p(E | H) is the probability that the power supply is has a noisy fan given that it is defective..
Question 4 – Probability distribution
Study point - calculating Mean and Variance
B. Similar problem
Q. A psychologist kept a large population of rats. Each rat was to be observed individually running a maze. If a
rat had a tendency to turn right in the maze, it was given a score X=1. However, it the rat had a tendency to turn
left, it got a score X= 2. If any of the population of rats had equal probability of being a “right-turner” or “leftturner,” find population distribution of X. Find the means and variance of this distribution.
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