Instructions For each question, your answer must be based on an analysis of cond
ID: 3241720 • Letter: I
Question
Instructions For each question, your answer must be based on an analysis of conditional probability and/or independence. You must state each event relevant to the problem under consideration, and the formulas you use. Just writing down an answer or calculation without basing it on the relevant formula(s) on probability and conditinoal probability will earn zero credit (even if the answer is correct).
Problems 3 and 4 are based on the following table, which shows the stock market performance of 40 industries from five sectors of the U.S. economy as of noon on September 11, 2015.[1] (Take S to be the set of all 40 industries represented in the table.)
Increased (X)
Decreased (Y)
Unchanged (Z)
Totals
Financials (F)
3
4
1
8
Manufacturing (M)
8
3
3
14
Information Technology (T)
6
1
0
7
Health Care (H)
4
1
1
6
Utilities (U)
3
1
1
5
Totals
24
10
6
40
3. Calculate the following probabilities for an industry selected at random from all those represented in the table:
(a) That its stock market performance increased, given that it was a manufacturing industry.
(b) That it was a manufacturing industry, given that its stock market performance increased.
(c) That it was a manufacturing industry and its stock market performance increased.
(d) That it was a manufacturing industry or its stock market performance increased.
[Hint: See Exercises 69–73 in Section 7.5 of the textbook.]
4. Test the following pairs of events for independence:
(a) Z, M
(b) X, U
(c) Does the fact that a selected industry is a manufacturing industry make it more or less likely that its stock market performance increased?
Increased (X)
Decreased (Y)
Unchanged (Z)
Totals
Financials (F)
3
4
1
8
Manufacturing (M)
8
3
3
14
Information Technology (T)
6
1
0
7
Health Care (H)
4
1
1
6
Utilities (U)
3
1
1
5
Totals
24
10
6
40
Explanation / Answer
a)probabilities That its stock market performance increased, given that it was a manufacturing industry=8/14=4/7
b)That it was a manufacturing industry, given that its stock market performance increased=8/24=1/3
c)That it was a manufacturing industry and its stock market performance increased.=8/40=1/5
d)That it was a manufacturing industry or its stock market performance increased.=(24+14-8)/40=30/40=3/4
4)
a) here P(Z & M)=3/40
and P(Z)*P(M)=(6/40)*(14/40)=21/400
as P(Z & M) and P(Z)*P(M) are not both equal hence Z and M are not independent.
b)
P(X & U)=3/40
P(X)*P(U)=(24/40)*(5/40) =3/40
as P(X)*P(U) and P(X &U) both are equal ; X and U are independent.
c)
it makes more likely that its stock market performance increased as its probability =8/14 is greater then probabilty of its decrease which is (3/14)