this is what i understand this to be:
x p(x) p(x)*x (x-mean)^2 (x-mean)^2*p(x)
0 0.6274 0 0.19333609 0.121299063
1 0.3102 0.3102 0.31393609 0.097382975
2 0.0575 0.115 2.43453609 0.139985825
3 0.0047 0.0141 6.55513609 0.03080914
4 0.0001 0.0004 12.67573609 0.001267574
mean >>>>> 0.4397
variance >>>> 0.390744576
standard deviation >>>> 0.625095654
mean is .4397
standard deviation is .625095654 which is the square root of the variance.
mean is calculated as x occurrences times the probability of x occurrences.
these are then all added up to get the mean.
variance is calculated as follows:
first you get x occurrences minus the mean.
then you square that.
then you multiply that by the probability of x occurrences
these are then all added up to get the variance.
than you take the square root of the variance to get the standard deviation.