3. Bivariate distributions

Jessica is saving to buy her significant other a gold watch for Valentine's Day. Jessica works two jobs, a day job at a retail store and a night job at a movie theater. Jessica's monthly income at each job can take on one of three values because her hours worked at each job only assume three values. Define X as Jessica's monthly income from her day job and Y as Jessica's monthly income from her night job. Jessica's total income varies according to the following bivariate probability distribution.

			y
		114	279	444
	104	0.30	0.22	0.33
x	254	0.04	0.02	0.06
	404	0.00	0.01	0.02

XX= , and YY=

XX= , and YY=

The covariance of X and Y is . The coefficient of correlation is . The variables X and Y independent.

The expected value of X + Y is , and the variance of X + Y is .

In order for Jessica to afford the gold watch for Valentine's Day, Jessica's total income must be at least $533 next month.

What is the probability that Jessica can afford to buy the gold watch?

0.44

0.45

0.41

0.40

Chebysheff's Theorem states that the proportion of observations in any population that lie within k standard deviations of the mean is at least 1 - 1 / k (for k > 1).

According to Chebysheff's Theorem, there is at least a 0.75 probability that Jessica's total income for next month is between and .