Statistics basic question: Probability distrbution

[tamintl]

Homework Statement

A random variable X has three, and only three, possible values, 0; 2; 4
with the following probability distribution:

Probability:
Getting a 0 is 0:7

Getting a 2 is 0:1

Getting a 4 is 0:2

Let X₁ and X₂ be two independent random variables with this distribution.

(a) Determine the probability distribution for

X(bar)₂ = (X₁ + X₂)/2
and use this distribution to determine the expectation and variance of X(bar)₂

(b) Determine the expectation and variance of X and verify that the
variance of X(bar)₂ is one-half the variance of X.

Homework Equations

The Attempt at a Solution

X₂(bar) = 0 with probability 0.49
X₂(bar) = 1 with probability 0.14
X₂(bar) = 2 with probability 0.29
X₂(bar) = 3 with probability 0.04
X₂(bar) = 4 with probability 0.04

not sure how to work out the variance?

Regards as always
Tam

 

[Ray Vickson]

Homework Statement

A random variable X has three, and only three, possible values, 0; 2; 4
with the following probability distribution:

Probability:
Getting a 0 is 0:7

Getting a 2 is 0:1

Getting a 4 is 0:2

Let X₁ and X₂ be two independent random variables with this distribution.

(a) Determine the probability distribution for

X(bar)₂ = (X₁ + X₂)/2
and use this distribution to determine the expectation and variance of X(bar)₂

(b) Determine the expectation and variance of X and verify that the
variance of X(bar)₂ is one-half the variance of X.

Homework Equations

The Attempt at a Solution

X₂(bar) = 0 with probability 0.49
X₂(bar) = 1 with probability 0.14
X₂(bar) = 2 with probability 0.29
X₂(bar) = 3 with probability 0.04
X₂(bar) = 4 with probability 0.04

not sure how to work out the variance?

Regards as always
Tam

You have the probability distribution of $\bar{X}_2.$ Just apply the _definition_ of variance and the formulas for it that you can find in any relevant book, or on-line if you look.

RGV