Question 335:

Asked on August 10, 2008

Tags: Standard Deviation , Expected Value , Random Variable

1

Answer:

No answer provided yet.

The mean of a random variable is the expected value over the long term. To find it you simply sum the values of x times their probability of occurrence:

1(.5) + 2(.2) + 3(.1) + 4(.1) + 5(.1) = 2.1

To find the standard deviation, you follow the same procedure you would if the variable was continuous. Subtract each value from the mean (the value you just calculated), square the difference, then multiply the probability times that results. Finally take the square root of the result.

(1-2.1)² * .5  +  (2-2.1)² * .2  +  (3-2.1)² * .1  +  (4-2.1)² * .1  + (5-2.1)² * .1 =   1.89

1.89 is the variance of the distribution, the square root of 1.89 = 1.37 and is the standard deviation.