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- A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability 0.3, and his second will lead independently to a sale with probability 0.6. Any sale made is equally likely to be either for the deluxe model, which costs $1000, or the standard model, which costs $500. Determine the probability mass function of X, the total dollar value of all sales.Let X = daily number of bag of rice a farmer harvest. The farmer modeled X and got the following probability mass function. X 0 1 2 3 4 P(X=x) 0.1 0.4 0.25 0.15 0.10 a. The probability that the farmer will harvest 5 bags of rice today is? b. The probability that the farmer will harvest at least 2 bags of rice today? c. The amount of bags of rice the farmer harvest for a day on the average is? d. If the farmer gets $300 per bag, what is the farmer's average daily earnings? e. What is the variance of X?Suppose that a die is rolled twice. Let X be the minimum value to appear in the two rolls. Construct the table of the probability mass function of X. W Obtain the distribution function of X. Write out the moment generating function. Using the second factorial moment of X, compute the variance.
- Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?A coin is weighted such that P(H) = 3/4 and P(T) = 1/4. This coin istossed four times. Let X be the total number of heads. Find the probability mass function of X, and its expectation, variance, and standarddeviation.A roulette wheel has thirty slots consisting of two blue, eight white, and twenty red slots. You will receive P100 if the roulette stops spinning on a blue slot, P50 on a white slot, and nothing on a red slot. Let X be the amount you will receive as shown on the slot where the roulette stops spinning. Give the probability mass function of X. O x 100 50 f(x) 2/30 8/30 20/30 100 50 f(x) 1/15 4/15 5/15 100 50 f(x) 1/15 14/15 100 50 f(x) 1/3 1/3 1/3
- Find the mean and variance of X given the following probability density function:Given the joint probability density function of the two random variables X & Y then the variance of x = 2 0.12 0.04 0.04 1 0.08 0.19 0.05 2 0.06 0.12 0.30 O 0.128 O None O 0.224 O 0.602(i) Attempt the following questions. Show all necessary steps. Read the questions carefully. (ii) Any copied material from internet or your class fellows will get you ZERO marks. Q. 1 Let X be the number of bugs in the first draft of a piece of software, and let Y be the number of bugs remaining in the second draft of the same software. Their joint probability mass function is given by the following table: Y 0. 1 3 0. 0.03 0.14 0.09 0.08 1 0.05 0.10 K 0.04 0.04 0.09 0.08 0.09 (i) Obtain K so that it is the joint probability mass function; (ii) Find cumulative distribution function Fyy (x, y); (iii) Find the following probabilities using cdf obtained above (a) P(X 4), (c) P(X + Y > 3), (e) P(X < 3,Y < 2) 21
- Answer the last threeIn each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.) USE SALT (a) (c) = 0.9857 2.189 (b) P(0 ≤Z≤ c) = 0.3133 0.89 (c) P(C ≤ Z) = 0.1335 1.11 You may need to use the appropriate table in the Appendix of Tables to answer this question.In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: y 0.10 0.11 0.05 0.17 0.23 0.08 2 0.06 0.14 0.06 Find P(X = land Y = 0). a. Find P(X 2 land Y 1). b. C. d. Find the probability that the standard for ozone is exceeded at least once. Find the probability that the standard for particulate matter is never exceeded. e. f. Find the probability that neither standard is ever exceeded. g.
