Question

A particular store sells clothes dryers for three different prices, $500, $750, and $1000 (Random variable Y). They also offer a warranty that costs $150 regardless of dryer bought (Random variable X). The table below gives the joint probability table.

p(x,y)		Y
		$500	$750	$1000
X	$0	.35	.10	.05
	$200	.05	.15	.30

1. What is ?(? ≥ 100)?

2. A random customer comes into the store and buys a dryer. What is the expected value of the

   transaction (transaction includes both dryer type and warranty decision)?

3. What is the correlation coefficient?

4. What does this correlation coefficient tell you?

Show all work please

Answer 1

a)

	500	750	1000
0	0.35	0.1	0.05
200	0.05	0.15	0.3

?(? ≥ 100) = 1

b)

X	P(X)	X*P(X)
500	0.35	175.000
750	0.1	75.000
1000	0.05	50.000
300	0.05	15.000
550	0.15	82.500
800	0.3	240.000

mean = E[X] = Σx*P(X) =            637.5

c)

correlation=cov(x,y)/√(Var(x)*Var(y)) =           

   13750.00   /√(   10000.000   *   46718.750   )=   0.6361

d)

It means if you provide warranty, there are more chance of selling