STATS PLEASE HELP This is just a practice midterm not graded!! ASAP Q3 - Q8

Remark: You may find you need calculator for the practices here. But for the mid-exam, the questions will require simpler computation so that you will not need calculator. Q1. State what are conditional probability, independence, pmf, cdf, expec- tation and variance. 22. What are the pmf, cdf (if applicable), expectation, variance and stan- dard deviation to the following distributions. (a) Bernoulli; (b) Geometric; (c) Binomial; (d) Hypergeometric; (e) Negative binomial; (f) Poisson. Know how to read the cdf table for binomial distribution and Poisson distribution in Ap- pendix table A.1 and A.2 of the textbook. Q3. 2. A box contains 6 apples, 4 oranges, and 2 pears. Suppose 3 fruit are randomly selected. a) (8 pts) Determine the probability that exactly 2 are apples. b) (8 pts) Determine the probability that all 3 are of the same type. c) (8 pts) Determine the probability that 1 of each type is selected. d) (8 pts) If fruit are selected one by one until a pear is found, determine the probability that at least 6 selections are required. Q4. 3. (20 pts) Medical screening of a population is proposed to detect a disease. The probability that the diagnostic test correctly identifies someone with the disease as positive is .99, and the probability that the test correctly identifies someone without the disease as negative is .95. The incidence of the disease in the general population is .0001. If the result of the test is positive for someone, what is the probability that the person has the disease? If the result is negative, what is the probability that the person does not have the disease? Q5. 3. (20 pts) The probabilities that 3 computers, A, B, and C, crash on any given day are 5/9, 2/3, and 3/4 respectively. The probabilities that they will crash after 5 pm are .025, .02, and .01 respectively. If a computer crashes after 5 pm, what is the probability that it is computer B? Q6. 4. At the Megamart Department Store the probability of encountering a cashier without a line is 1/10. From a random sample of 16 cashiers, determine: a) (10 pts) the expected number of cashiers without a line b) (10 pts) the probability that between 4 and 8 cashiers inclusive don't have lines c) (10 pts) the probability that between 5 and 9 do have lines Q7. 2.b. (6 points) Let X be a discrete random variable with the probability mass function below. Find / and o. You must show how you got each of your answers. P ( X = x ) 35 35 35 Q8. Suppose X is the same random variable as in Q7, find E(X?), E(X3), E(1 + 2X + 3X2), V(X) and V(5X + 8)