Answer
Standard deviation equals 1.22
Work Step by Step
Step 1
Find the expected value of X from the data. which is found by the equation
(X)*(p)+(X)*(p)
X being the value
and p being the probability
for this data expected value would by found by
(0)*(.5)+(1)*(.2)+(2)*(.2)+(3)*(.1)=.9
Expected value of X is .9
Step 2
to find the variance the equation is
$(x1-E(X))^2*(p1)+(x2-E(X))^2*(p2)$
where x is the data
E(X) is the expected value and p is the probability
so the equation would be
$(0-.9)^2*(.5)+(1-.9)^2*(.2)+(2-.9)^2*(.2)+(3-.9)^2*(.1)$
Which equals 1.49
1.49 is the variance
Step 3
to find the standard deviation find the square root of the variance
$\sqrt 1.49$
Standard deviation equals 1.22
