1. Consider the probability distribution below. (30 points)

Probability	X (lb.)
0.1	0
0.3	0.5
0.5	1
0.1	5

1. Compute the expected value. Describe your computation procedure. And interpret your finding. (10 points,5 points for description of the computation and 5 points for interpretation)
2. Compute the variance. Describe your computation procedure. (5 points)
3. Compute the standard deviation. Describe your computation procedure. And interpret your finding. (10 points,5 points for description of the computation and 5 points for interpretation)
4. Considering the fact that X is measured in pounds (lb.), what are the units of measurement for expected value, variance, and standard deviation? (5 points)

1. Let's add variable Y, measured in dollars, to the probability distribution table in Question No. 1. (40 points)

Joint Probability	X (lb.)	Y ($)
0.1	0	0
0.3	0.5	100.55
0.5	1	195.75
0.1	5	400

1. Before you even compute the coefficient of correlation between X and Y, what do you expect of its sign: is it likely to be greater than zero or less than zero? Explain your answer in one short paragraph (less than 100 words). (5 points)
2. Follow the formula below to compute the covariance between X and Y: