   SEARCH HOME Math Central Quandaries & Queries  Question from Patrick, a student: Here's a question i can't figure out: a small airline company has only three flights per day. The number of delayed flights per day is regarded as a random variable, and i'm supposed to calculate the expected value and standard deviation of the number of delays. the probability distribution looks like: No. of Delays: 0 1 2 3 Prob. of delay: 05. 0.3 .1 .1 Hi Patrick,

I am going to look at a different example. Suppose I have 5 coins in my pocket, one worth 25 cents, two worth 10 cents each and two worth 5 cents each. I select a coin at random and the random variable X is the value of the coin I select. The probability distribution is then

 X: Value of the coin Probability 5¢ 10¢ 25¢ 2/5 2/5 1/5

To find the expected value of a random variable you multiply each possible value of the variable by the probability that you obtain that value and then add the resulting numbers. Thus the expected value of X is

E(X) = 5¢ × 2/5 + 10¢ × 2/5 + 25¢ × 1/5 = 55/5 = 11¢

The standard deviation of a random variable is the square root of the variance and the variance is defined as the expected value of the random variable (X - E(X))2. For my example E(X) = 11¢ and hence the random variable (X - E(X))2 and its probability distribution is given by

 (X - E(X))2 Probability (5 - 11)2 = 36 (10 11)2 = 1 (25 - 11)2 = 196 2/5 2/5 1/5

Thus

Variance(X) = 36 × 2/5 + 1 × 2/5 + 196 × 1/5 = 270/5 = 54

and

Standard Deviation(X) = √54 = 7.35¢     