# 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.

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.

##### 1 Answer

May 17, 2018

#### Explanation:

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

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