a) for each of the four datasets "guess" what the correlation coefficient is.
b) for dataset 1 "guess" what the least squares regression line is.
Problem 1:
Consider the following dataset:
| x | 23 | 45 | 17 | 31 | 39 | 29 | 27 | 35 | 35 | 30 |
| y | 40 | 100 | 35 | 55 | 45 | 25 | 40 | 60 | 72 | 60 |
Problem 2 A box contains 4 blue balls and 10 red balls.
a) One ball is picked from the box. The rv X is 1 if the ball is blue, 0 if it is red. Find the probability mass function of X.
b) Say the first ball is put aside and a second ball ball is picked from the box. Let the rv Y be the number of balls picked that are blue. Find the probability mass function of Y.
Problem 3 It is known that in a certain population 45% of the people are male.
a) If we randomly select 75 people from this population, what is the mean and the standard deviation of the number of females in the sample?
b) if we randomly select one person after the other, what is the probability that the first male selected is the fourth person?
c) if we randomly select 8 people from this population, what is the probability that exactly 5 of them are female?
Problem 4 A box contains 5 red balls, 5 blue balls and 5 green balls. You pick two balls from the box at the same time. One possible outcome of this experiment is (r,b), that is we drew one red and one blue ball.
a) What is the sample space for this experiment?
b) What is the probability that the two balls drawn have the same color?
c) Say the box contains 5 red balls, 5 blue balls and 3 green balls, what is the sample space then? Now it is not possible (for us) to find the probability of both balls are the same color. Why?
Problem 5 Consider the four datasets in the following scatterplots:
a) for each of the four datasets "guess" what the correlation coefficient is.
b) for dataset 1 "guess" what the least squares regression line is.