Exercise 1 Let suppose that 70% of voters in New York Vote for Hillary Clinton in the 2016 presidential election. By considering 10 friends living in New York City: How many of this group of friends would you expect to have voted for Hilary? (Expected value) Suppose that all of them indicated that they voted for Hillary. Determine the probability of this assuming they are representative (sample) of all New York voters. 8 among them voted for Hillary. Determine the probability that at least 8 of them would vote for Hilary if they are representative (sample) of all New York voters,
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Exercise 1
Let suppose that 70% of voters in New York Vote for Hillary Clinton in the 2016 presidential election. By considering 10 friends living in New York City:
- How many of this group of friends would you expect to have voted for Hilary? (Expected value)
- Suppose that all of them indicated that they voted for Hillary. Determine the probability of this assuming they are representative (sample) of all New York voters.
- 8 among them voted for Hillary. Determine the probability that at least 8 of them would vote for Hilary if they are representative (sample) of all New York voters,
Exercise 2
At a public seminar hold by a financial company, a managing partner discussed investment risk analysis. She discussed how a coefficient of variation (refer to chapter 3 to review the coefficient of variation.) To demonstrate her point, she used two hypothetical stocks as examples. She considered x to be equal to the change in assets for a $1,000.00 investment in stock A and y the change in assets for a $1,000.00 investment in stock B. The following probability distributions were presented to the audience.
|
X |
P(x) |
Y |
P(y) |
|
-$1,000.00 |
0.10 |
-$1,000.00 |
0.20 |
|
0.00 |
0.20 |
0.00 |
0.40 |
|
500.00 |
0.30 |
500.00 |
0.30 |
|
1,000.00 |
0.30 |
1,000.00 |
0.05 |
|
2,000.00 |
0.10 |
2,000.00 |
0.05 |
Please use two different tables, one for variable x and one for variable y, to answer the following questions. Put the result of each variable below its table. I have to see all your calculations in each the table
- Compute the
expected values for random variable x and y: E(x) and E(y) - Compute the standard deviations for random variable x and y: σx and σy
- Recalling that the coefficient of variation is determined by the ratio of the standard deviation to the mean, compute the coefficient of variation for each random variable. CVx and CVy
- Referring to part c, suppose the seminar director said that stock A was riskier since its standard deviation was greater than the standard deviation of stock B. How would you respond? (hint: What do the coefficients of variation imply?)
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