Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20 second time period, is characterized by the fallowing discrete probability function e-6 x 6* f(x) = for x = 0, 1, 2, 3... x! Find the probability that in a specific 20-second time period, less than 3 cars arrive at the inter-section. A) 0.05949 B) 0.06197 c) 0.14873 D) 0.15120
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- The inter-arrival time of customers into a bank is exponentially distributed with a mean of u minutesA a) What is the probability that the inter-arrival time of a random customers is more than 6 minutes? [ b) What is the probability that the inter-arrival time of a random customers is less than 4 minutes? [15. The probability that a regularly scheduled flight departs on time is P(D) = 0.81; the probability that it arrives on time is P(A) = 0.85; and probability that it departs and arrives on time is P(DNA) = 0.75. Find the probability that a plane i) Departed on time, given it has arrived on time. ii) Arrives on time , given that it departed on time iii) Departed on time, given has not arrived on time.It is known that the average lifetime of a central processing unit (CPU) of a server is eight years and shows an exponential distribution. What is the probability that the company that leases the server for five years will encounter a central processing unit (CPU) failure within the lifetime? a)0.465 b)0.395 c)0.535 d)0.606 e)no one
- The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20-39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20-39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. P(X > 122)%3D eal limir thaor tnr the hinamialdietrikotian tn indtha neohabilin: tbot the numbar of individuale in Aanly tha nd tems of use contact us he p about us cyeers 6:56 PM 11/6/2020 a. 2) Cip prt sc insert 110 |Suppose that a point is randomly chosen from a segment with a length of 12 units. What is the probability that no of two smaller segments is smaller than 2/3 units? ROUND OFF your answer in DECIMAL FORM (4 decimal places)The amount of time it takes Alice to make dinner is continuous and uniformly distributed between 10 minutes and 46 minutes. What is the probability that it takes Alice more than 42 minutes to finish making dinner given that it has already taken her more than 32 minutes in the making of her dinner?
- 12. The number of new individuals in a population of animals is sometimes approximated calculating the expected number of survivors of the new born animals from the next genera- tion. The idea is that the number of new animals born follows some probability distribution, and the number of animals that survive depend on how many are present.¹ One example of a survivor function is the following: S₁(k) = b.ck, where b and c are real numbers with 05. Assume that X is a discrete random variable with cumulative distribution function (cdf) F(x) given below. F(X) 0-8 0.b t0.2 -2 2 3 ->2. The number of meteors found by a radar system in any 30-second interval under specified a. What is the probability that at least one meteor is found in a one-minute interval? ne meteors appear randomly b. Determine x such that the probability no meteor is found in x-minute interval is 0.02. UTM M UTM UTM c. If there is no meteor appear after two-minute interval, what is the probability that it UTM will appear in the next one and a half-minute interval? m UTMCalculate the following probabilities: 1. P(16155. The total amounts for claims during each unit period in the risk process at discrete time has been modeled by means of a discrete random variable Y with values in the set {0, 1, ...} and it has been assumed that the expectation of this variable is finite. Show that 00 E(Y) = E F(y). y=0Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON