59.4k views
5 votes
A fair spinner split evenly into 4 spaces has the values 2,5,6 and 10. find the variance

1 Answer

3 votes

Let
X denote the value the spinner lands on. Then
X has PMF


P(X=x)=\begin{cases}\frac14&\text{for }x\in\{2,5,6,10}\\\\0&\text{otherwise}\end{cases}

Then the average value the spinner lands on is


E[X]=\displaystyle\sum_xx\,P(X=x)=\frac{2+5+6+10}4=\frac{23}4

and the variance is


V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2

We have


E[X^2]=\displaystyle\sum_xx^2\,P(X=x)=\frac{2^2+5^2+6^2+10^2}4=\frac{165}4

so that the variance is


V[X]=\frac{165}4-\frac{23}4=\frac{71}2

User Manub
by
7.5k points