Question

Give the standard deviation for the probability distribution. (round to two decimal places)

Answer 1

Firstly $\text{Var}[X]=E[X^2]-(E[X])^2 \\ E[X^2]=\sum x^2\Pr(X=x) \\ E[X] = \sum x\Pr(X=x)$.

So work out E[X],
$E[X]=(1\times0.20)+(2\times0.30) + (3\times0.10) + (4\times 0.20)+(5\times0.05)$, note we can get rid of the 0 because 0 times anything = 0

Similarly, work out E[X²]
$E[X]=(1^2\times0.20)+(2^2\times0.30) + (3^2\times0.10) + (4^2\times 0.20)+(5^2\times0.05)$, note we can get rid of the 0 because 0 times anything = 0.

Then Var[X] = 6.75 - 2.15² = 2.1275
By using $\text{SD}[X] = \sqrt{\text{Var}[X]}$ you find SD=[X]=1.46