Question

Practice problems in my statistics textbook I can't find answers for to verify mine:

A regular six-faced fair die will be rolled. Let Y be the number obtained.

a.) What is the expected value of Y?

b.) What is the variance of Y?

Answer 1

Solution:
Expected value can be calculated as

Y	P(Y)	Y*P(Y)
1	1/6	1/6
2	1/6	2/6
3	1/6	3/6
4	1/6	4/6
5	1/6	5/6
6	1/6	6/6

So Expected value is (1/6) +(2/6)+(3/6)+(4/6)+(5/6)+(6/6) = 0.1666+ 0.3333 + 0.5 + 0.6666 + 0.8333 + 1 = 3.4998

So expected value for this is 3.4998
Solution(b):
Variance of Y can be calculated as

Summation(Y-E(Y))^2 *P(Y)

Y	P(Y)	Y*P(Y)	Y-E(Y)	(Y-E(Y))^2	(Y-E(Y))^2 *P(Y)
1	1/6	0.1666	-2.4998	6.24900004	1.041083406664
2	1/6	0.3333	-1.4998	2.24940004	0.749725033332
3	1/6	0.5	-0.4998	0.24980004	0.12490002
4	1/6	0.6666	0.5002	0.25020004	0.166783346664
5	1/6	0.8333	1.5002	2.25060004	1.875425013332
6	1/6	1	2.5002	6.25100004	6.25100004
	Xbar	3.4998	Sum(Y-E(Y))^2 * P(Y)	10.208916859992

SO variance of Y= 10.20891685