Question

1. An oil company is considering whether to invest in a project. After some analysis it concludes that the price of oil will be either $100 or $70 and that production rates will be either 100 or 200. The joint distribution of the two random variables (i.e., the probabilities) is given in this table.

		Price
		$70	$100
Production	100	.25	.25
	200	.25	.25

1. Calculate the expected value and standard deviation of price and production
2. Calculate the covariance and correlation between price and production

Answer 1

a) The expected values here are computed as:
E(Price) = 0.5*(70 + 100) = 85
E(Production) = 0.5*(100 + 200) = 150

Therefore 85 and 150 are the expected values for Price and Production here.

E(Price²) = 0.5*(70² + 100²) = 7450
E(Production²) = 0.5*(100² + 200²) = 25000

The standard deviation now for price and production here are computed as:

Therefore 15 and 50 are the standard deviations for Price and Production here.

b) The expected value here is computed as:

E(Price*Production) = 0.25*(7000 + 10000 + 14000 + 20000) = 12750

Cov(Price, Product) =  E(Price*Production) - E(Price)E(Production) = 12750 - 85*150 = 0

As the covariance here is 0, therefore the correlation coefficient between Price and production is also 0.