Calculate the expected value and standard deviation of X, the number of on the job accidents:
Accidents 0,1 2 Probability .5, ?, .2
P(X=1) =
E(x) = µx =
Standard deviation =
Note: Your ? value should be .3 because each probability will then add to 1.
To find the mean:
SUM [x * P(x)]
Multiply each x by its respective probability P(x). Add together for a total. This will be your mean.
To find variance:
SUM [x^2 * P(x)] - mean^2
Square each x. Multiply each squared x by its respective probability P(x). Add together for a total. Square the mean. Subtract the squared mean from the total. This will be your variance.
To find standard deviation:
Take the square root of the variance.
Hopefully, this information will help you with other problems of this type.