Marketing estimates that a new instrument for the analysis o

Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product.

Find Var(X^2 ).

Solution

Defining the random variable:
X = the yearly revenue (millions of dollars) of the product
Since the random variable, X, has a finite (or countably infinite) range, it