If the lifetime of a computer is an exponential random variable whose mean is 5 year. Given that the computer has not broken down after 3 years, find the expected total lifetime of this computer. (a) 4 (b) 6 (c) 8 (d) 10
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- The lifetime T (in years) for a particular type of electric toothbrush is assumed to have the probability density f given by t 0 ≤ t ≤6 f(t) = {+ 3 18 otherwise.Show that the multiplication law P(AB) = P(A/B) P(B), established for two events, may be generalized to three events as foilows; %3D P(AOBOC) = P(A/BC) P(B/C) P(C)The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 16-year period. Assume each year is independent. Part (a) Part (b) List the values that X may take on. X=0, 1, 2,..., 15, 16 OX= 1, 2, 3, OX= 1, 2, 3, OX=1,2,3,... 15, 16 98, 99, 100 Part (c) Give the distribution of X X-B 0.02 □ Part (d) How many audits are expected in a 16-year period? (Round your answer to two decimal places.) 0.32 audits Part (e) Find the probability that a person is not audited at all. (Round your answer to four decimal places.) Part (1) Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)
- Users are connected to a database server through a network. Users request files from the Database server. The database server takes a period of time that is exponentially distributed with mean 5 seconds to process a request.Find the probability that 10 requests are processed by the server during the first 1 minutes Determine the probability that no request is processed by the server during the first 2 minutes Determine the average number of requests processed in 2 minutesBased on a survey, assume that 33% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when six consumers are randomly selected, exactly three of them are comfortable with the drones. What is wrong with using the multiplication rule to find the probability of getting three consumers comfortable with drones followed by three consumers not comfortable, as in this calculation: (0.33)(0.33)(0.33)(0.67)(0.67)(0.67) = 0.0108? Choose the correct answer below. A. The event that a consumer is comfortable with drones is not mutually exclusive with the event that a consumer is not comfortable with drones. B. The probability of the second consumer being comfortable with drones cannot be treated as being independent of the probability of the first consumer being comfortable with drones. O C. There are other arrangements consisting of three consumers who are comfortable and three who are not. The probabilities corresponding to those other…Suppose a slot machine has three independent wheels as shown in the figure below. The payoffs for the slot machine shown in the figure are in the following table. First one cherry 4 coins First two cherries 6 coins First two wheels are cherries and the third wheel a bar 11 coins Three cherries 11 coins Three oranges 14 coins Three plums 14 coins Three bells 20 coins Three bars (jackpot) 50 coins What is the mathematical expectation for playing the game with the coin being a quarter dollar? Assume the three wheels are independent. (Assume you are playing one coin. Round your answer to two decimal places.)
- Suppose 5 students are going to take a test independently from each other and that the number of minutes that any student needs to finish the exam has an exponential distribution with mean 80.If the test starts at 9 a.m., determine the probability that at At least one of the students finishes the exam before 9:40 am.Scenario 1: A surgeon routinely performs 4 surgeries. The chance that he performs surgery “A” is 30%. A random sample of 15 patients is selected. Let the variable X be defined as the number of patients that have surgery "A". Scenario 2: Thirteen (13) cards are randomly selected from a standard deck of cards without replacement. Let the variable X be defined as the number of spades selected. Directions: Pick a scenario describe a binomial experiment. Recall the random variable X is for the number of successes in a binomial experiment. • Be certain to state the criteria for a binomial distribution and how it does or does not meet each of the five conditions. Once your answer is posted, you will be able to see your classmates' responses.A certain insecticide kills 80% of all insects in laboratory experiments. A sample of 6 insects is exposed to the insecticide in a particular experiment. Assume the binomial situation. What is the probability that exactly one insect will die? P(X=1)?
- Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…An average of 1 package is sent to a server in 1 second. The server, on the other hand, uses the 5 packages that come to it.is preparing a document. The time between packets is modeled as an exponential random variable. X of the serverLet it be a random variable expressing the time it takes to prepare a document. Passing for the preparation of a documentyour timea. Find the probability that it is more than 10 seconds.b. Find the probability that it is between 5 seconds and 10 seconds.
