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

Question

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.

9976 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-17T02:32:53

$"variance" = 23.182$

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
$color(blue)("variance" = 23.1819)$