B: Solve the following problems. Type your solution. (Subtotal: 18 points) - Use the following information for problems 1 4: From a collection of components, three are selected and checked for being defective or not. Let the random variable X be the number of defective components. 1. Determine the probability mass function f(x). 2. Determine the cumulative distribution function F(x). 3. Find the expected value E(X). (3 points) (3 points) (3 points) 4. Find the variance V (X) and standard deviation of X (5 points) 5. A particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. a) Over 5 mornings, what is the probability that the light is green on exactly 1 day? b) Over 20 mornings, what is the probability that the light is green on exactly 4 days?