To find the mean for a random variable

To find the mean for a random variable we multiply each possibility by its probability and then we add them together. The symbol for the mean of a random variable is E(X), pronounced "E of x" the short way and "Expected Value" the long way.

Like this:

X = {1, 2, 3, 4, 5, 6}

P(1) = 0.400

P(2) = 0.200

P(3) = 0.100

P(4) = 0.150

P(5) = 0.050

p(6) = 0.100

E(X) = 1*0.400 + 2*0.200 + 3*0.100 + 4*0.150 + 5*0.050 + 6*0.100

= 0.400 + 0.400 + 0.300 + 0.600 + 0.250 + 0.600

= 0.800 + 0.900 + 0.850

= 1.700 + 0.850

= 2.650

Thus the mean is 2.650. Notice that this isn't even one of the values in the set { }. That's okay. We still use it and say that on average we can expect to have 2.650 or whatever these things are we're discussing.

Please invent a random variable (be sure it follows the rules which say the probabilities must add to 1 and that they must be between 0 and 1 inclusive). Or find a random variable in the text.

Then find E(X) showing all the steps.