Let X denote the number of empty bins when 60 balls are thrown independently into 30 bins. What is the expectation of X ?
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- Suppose the probability that a male develops some form of cancer in his lifetime is 0.4573. Suppose the probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51, and that this probability is independent of the probability that a male will develop cancer in his lifetime. • C = a man develops cancer in his lifetime• F = a man has at least one false positive Part (a) Construct a tree diagram of the situation. P(C) = P(F | C) = P(F | C' ) If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not. -You cannot assume the man has cancer because there is not enough information given. -You cannot assume the man has cancer because there is a 51% chance that the test is false. -You cannot assume the man has cancer because both the probability of developing cancer in his lifetime and the probability of…express the event "taking atleast 16 credits" in terms of X and find its probabilityA class contains 40 students. The probability of failing in one of the courses for each student is 0.03, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.04. All other fail reasons are low average. The examinations are private, so the results are mutually independent. Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester. Find the joint MGF
- A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore. A) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. B) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. C) Compute ?, the expected value of the number of fish caught per fisherman in a 6-hour period (round "at least 4" to 4). D) Compute ?, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round "at least 4" to 4).Construct the probability distribution for the random variable X which pertains to the number of heads when you toss three coins at the same time.For 10 percent of the products in a category, a firm fails to satisfy all demand during themonth. What is its in-stock probability?
- The probability of committing a type II error is denoted as â True or FalseThe flight from Greenville to Charlotte can take anywhere from 43 minutes to 68 minutes. Suppose the random flying times, X, are uniform from 43 to 68 minutes. What is the probability a flight last longer than 59? or P(X>59) Do not round.Let ? be the amount of time (in minutes) a postal clerk spends with his or hercustomer. The time is known to have an exponential distribution with the average amount of timeequal to four minutes.i) Find the probability that a clerk spends four to five minutes with a randomly selected customer.ii) Find the probability that a clerk spends at least five minutes with a randomly selected customer.
