The probability distribution of X is given in the table. What is the variance of the distribution?

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The probability distribution of X is given in the table. What is the variance of the distribution?

Mathematics
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start by finding the mean

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um .25?
|dw:1432817965592:dw|
do you mean `2.5` ?
mean = 1*.4+2*.1+3*.1+4*.4 = 2.5
yes 2.5 sorry.
good, find the deviation from mean for each of the data values
subtract mean from each data value
sub. 2.5 to each point?
Yes, work \(\large x_i - 2.5\) for each data value
|dw:1432818405802:dw|
-1.5, -.5, .5, 1.5
square each of them
\(\large (x_i-2.5)^2\)
-2.25, -.25, .25, 2.25?
|dw:1432818549729:dw|
when you square, the negative sign disappears thats precicely the reason we square here ok
(-1.5)^2 = +2.25 it is not -2.25
ops, crap. I put it in my calculator wrong then. :/
@rational so what do I do now?
hey still here ?
yeah.
sry was on mobile
okay where are we
Its okay :) 2.25 fix from negative to positive :)
|dw:1432819551531:dw|
multiply each of those by the corresponding probabilities, then add them up
|dw:1432819635519:dw|
1.85
Perfect! 1.85 is the variance
we basically used below formula |dw:1432819854547:dw|

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