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.

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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)#