Question

He following table shows the probability distribution for a discrete random variable. What is the variance of X?

X 11 14 16 19 21 23 24 29
P(X) 0.07 0.21 0.17 0.25 0.05 0.04 0.13 0.08

The mean of the discrete random variable X is 18.59.

Answer 1

`"variance" = 23.182`

Explanation:

The variance of X is equal to the standard deviation of X squared:

`"variance" = ("standard deviation")^2`

Refer to this link on mathisfun.com for details on calculating variance manually.

I used my TI-84+.

• Enter the data into two lists. Press "stat", then "enter" in order to edit the lists
• I used `L_1` for `X` and `L_2` for `P(X)`.
• Next, press "stat", move right to "calc", then "enter" in order to calculate 1-variable statistics on X.
• Confirm that `L_2` is the frequency list for `L_1`, and press "calculate".
• The screen should show the standard deviation `sigma_x = 4.8148`

Finally, square the standard deviation to get
`color(blue)("variance" = 23.1819)`