5) Let X represent the number of people in a household in the United States in 2021. X 1 2 3 4 5 6 7 or more P(x) 0.29 0.35 0.15 0.12 0.06 0.02 0.01 a) Find P(3) b) Find P(More than 4). c) Find the probability that a randomly picked household contains 6 people. d) Find the probability that a randomly picked household has less than 3 people. e) Compute the mean ux. f) Compute the standard deviation ox._ 6) An investor is considering a $25,000 investment in a start-up company. She estimates that she has a probability of 0.45 of a $60,000 loss, probability of 0.25 of a $40,000 profit, probability of 0.20 of a $15,000 profit, and probability 0.10 of breaking even (a profit of $0). a) Create a discrete probability distribution. b) What is the expected value of the investment? c) Would you advise the investor to make the investment? Explain why? 2