1. In-Class Exercise: Discrete Distributions
3-19. 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.
Determine the probability mass function, CDF, mean, and variance of X.

2. 3-21. An optical inspection system is to distinguish among different part types. The probability of a correct classification of any part is Suppose that three parts are inspected and that the classifications are independent.
Let the random variable X denote the number of parts that are correctly classified.
Determine the probability mass function, CDF, mean, and variance of X.