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Date Submitted: 12/06/2015 02:41 PM
For Students
Solutions to Odd-Numbered End-of-Chapter Exercises
*
Chapter 2
Review of Probability
2.1. (a) Probability distribution function for Y
Outcome (number of heads) | Y 0 | Y 1 | Y 2 |
Probability | 0.25 | 0.50 | 0.25 |
(b) Cumulative probability distribution function for Y
Outcome (number of heads) | Y 0 | 0 Y 1 | 1 Y 2 | Y 2 |
Probability | 0 | 0.25 | 0.75 | 1.0 |
(c) .
Using Key Concept 2.3:
and
so that
2.3. For the two new random variables and we have:
(a)
(b)
(c)
2.5. Let X denote temperature in F and Y denote temperature in C. Recall that Y 0 when X 32 and Y 100 when X 212; this implies Using Key Concept 2.3, X 70oF implies that and X 7oF implies
2.7. Using obvious notation, thus and This implies
(a) per year.
(b) , so that Thus where the units are squared thousands of dollars per year.
(c) so that and thousand dollars per year.
(d) First you need to look up the current Euro/dollar exchange rate in the Wall Street Journal, the Federal Reserve web page, or other financial data outlet. Suppose that this exchange rate is e (say e 0.80 Euros per dollar); each 1 dollar is therefore with e Euros. The mean is therefore
e C (in units of thousands of Euros per year), and the standard deviation is e C (in units of thousands of Euros per year). The correlation is unit-free, and is unchanged.
2.9. | | Value of Y | Probability Distribution of X |
| | 14 | 22 | 30 | 40 | 65 | |
| Value of X | 1 | 0.02 | 0.05 | 0.10 | 0.03 | 0.01 | 0.21 |
| | 5 | 0.17 | 0.15 | 0.05 | 0.02 | 0.01 | 0.40 |
| | 8 | 0.02 | 0.03 | 0.15 | 0.10 | 0.09 | 0.39 |
| Probability distribution of Y | 0.21 | 0.23 | 0.30 | 0.15 | 0.11 | 1.00 |
(a) The probability distribution is given in the table above.
(b) The conditional probability of Y|X 8 is given in the table below
Value of Y |
14 | 22 | 30 | 40 | 65 |
0.02/0.39 | 0.03/0.39 | 0.15/0.39 | 0.10/0.39 |...