Probability expected number and variance.

[Guest]

Evening all, I just wanted to see if I am on the right track with regards to my workings out.

I need to find the expected number of flaws and also the variance from the table.

Flaws- 0 ,1, 2, 3
Frequency- 5, 12, 27, 6
Probability- 0.10, 0.24, 0.54, 0.12

At the moment I have come up with - Expected value of flaws- E(X) = 0x0.10+1x0.24+2x0.54+3x0.12= 1.68 and for the Variance -(0-1.68)^2x.010+(1-1.68)^2x0.24+(2-1.68)^2x0.54+(3-1.68)^2x0.12= 0.6576.

Is this correct how I have worked out the expected value and variance as I have not used the frequency in any calculations which is what is concerning me?

Many thanks

[Guest]

Yes, that is correct. You don't need the frequency since that is "contained" in the probability.
5+ 12+ 27+ 6= 50
5/50= 0.10
12/50= 0.24
27/50= 0.54
6/50= 0.12