Question

A die is rolled twice. Let X1 and x2 be the outcomes, and let s= X1 + x2 be the sum of these outcomes. 1. What is the expected value of x1 and x2? 2. What is the standard deviation of x1 and x2? 3. What is the expected value and standard deviation of sA die is rolled twice. Let X1 and x2 be the outcomes, and let s= X1 + x2 be the sum of these outcomes.

1. What is the expected value of x1 and x2?

2. What is the standard deviation of x1 and x2?

3. What is the expected value and standard deviation of s

Answer 1

1)

X₁ and X₂ denote the outcome of the roll of a die. So, they would be identically distributed.

Probability distribution of X₁:

X1	1	2	3	4	5	6
P(X1)

So,

Similarly,

2)

Now,

and,

So,

Similarly

3)

Now,

and,

{Since X₁ and X₂ are independent}