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- МАТH1208 QUESTION 2 А. The table below shows the probability distribution of the likelihood of the number of SUVS in a household in Forest Hill, St Andrew. Number of 2 3 SUVS (x) P(X = x) 0.05 0.12 0.60 0.20 Find: i. The value of 'c' ( the probability of 4 SUVS in a household) ii. The expected value [E(X) ], the mean value of SUVS in a household iii. The variance iv. standard deviation of SUVS in a householdThe annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.4.2 The probability distribution of the discrete random variable X is f(x) = 3 (*)*** Find the mean of X. 3-x (¹)ª (²³)³—ª, x = 0, 1, 2, 3.
- Example 5-16. For the following probability distribution: dF yo, ex dx,-A bus company claims that the length of time a bus is late is uniformly distributed and the maximum time that a bus is late is 20 minutes. And the delay of a bus is independent of the other buses. Find the probability that 2 out of the next 5 buses are late for more than 12 minutes. (Pick the options closest to the answer.) 0.35 0.55 O 0.25 0.65 0.453. 4-5 Please solve the following with the provided informationSuppose we wish to estimate the expectation of a random variable X with a large popula- tion. We observe n members of the population, i.e. {x;}1. Individual i is included in the sample with a probability proportional to p;. Please demonstrate that the usual sample E; ®i/Pi i=1• mean ī = n-1E, xi is no longer a consistent estimator for E[X], but ã is. E; 1/Pj vi=12. The following probabilities are given for a certain life: 10P75 = 0.55, 20 P60 = 0.35, and = 0.65 15P 60 Evaluate (i) the probability that the life aged 60 will die between ages 75 and 85. (i the probability that the life aged 60 will die within age 80.3. 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 following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given. y p(y) 0 1 0.50 0.35 0.10 0.05 USE SALT 3 (a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.) (b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ≤ x ≤ b). Round your answer to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.Example 5-49. Let the p.d.f. of the random variable (x, y) be : a-² e-(x+y)/a ; x, y > 0, a > 0 f(x, y) = { , elsewhere Find the distribution of (X-Y).The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON