Math Is Fun Forum

MathstudentUK

Member

Registered: 2021-03-10

Posts: 1

Probability help (check my workings out please)

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(EV) of flaws- = 0x0.10+1x0.24+2x0.54+3x0.12= 1.68 and for the Variance = (0-1.68)^2 x .010+(1-1.68)^2 x 0.24+(2-1.68)^2 x 0.54+(3-1.68)^2 x 0.12= 0.6576.

Is this correct how I have worked out the expected value and variance?

Many thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,580

Re: Probability help (check my workings out please)

hi MathstudentUK

Welcome to the forum.

I've checked your working 2 ways and agree with your answers.  Well done!

Have a look at this link: https://www.mathsisfun.com/data/random- … iance.html

That formula also works out the variance.  Back in the days of simple calculators this formula had the advantage that you can work out the running total (x^2 times p) as you go, so you can keep running totals of ∑x and ∑x^2 as the data is input, then find both the mean and the variance at the end from the two sums and a count of how much data. With  frequencies the formula is

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob