What's the variance of this random variable?

Question

There's a random variable given:

$$\begin{array}{|c|c|} \hline \rm {X}_i & -2 & 0 & 2 & 4 \\ \hline \rm{p}_i & 0,1 & 0,5 & 0,3 & 0,1 \\\hline\end{array}$$

The variance I calculated is: 2.56 or 2.24 depending on what formula I use. This is weird and I want to verify.

The correct variance is $2.56$. Of course each method will give this. — André Nicolas, Dec 28 '13 at 08:14

score 2 · Accepted Answer · answered Dec 28 '13 at 08:19

2

Here is my calculation done two ways

$$ \sum x_k p_k = 0.8 ~~~ \hbox{and}~~~ \sum x_k^2 p_k = 3.2, ~~~ 3.2-0.8^2 = 2.56 $$

The other way is $$ \sum (x_k-0.8)^2 p_k = 2.56 $$

Sorry for using the decimal point instead of the comma!

answered Dec 28 '13 at 08:19

user44197

1 Answers1