Verify that the following function is a probability mass function, and determine the requested probabilities. Answer rounded-off to 4 decimal places f(x)=(125/31)(1/5)* P(X>1)= " x={1,2,3}
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- Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter a = 0.01437. (a) What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places.) at most 100m at most 200m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places.) (c) What is the value of the median distance? (Round your answer to two decimal places.)The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following table. Days until Probability Changes 1.5 0.05 0.25 0.35 0.20 0.15 3 4.5 7 Calculate the probability mass function of the days until change. *Answers should be in rational numbers with 2 decimal places.The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp (-x/3100)]/3100 for x > 0 and f (x) = 0 for x ≤ 0. Determine the probability that:(a) A component lasts more than 1180 hours before failure.(b) A component fails in the interval from 1180 to 2010 hours.(c) A component fails before 3010 hours.(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean.Round your answers to three decimal places (e.g. 98.765).
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- What is the probability that x is less than 3, given the function below? 1 f(x) = -x/3 е 0.1226 0.3679 0.6321 0.8774 O O O OI need help with this probability density function problem. It asks to calculate the probability that the battery lasts longer than 1 hour. Please show work so that I can understand future problems like this.The multinomial joint probability mass function becomes the binomial probability mass function when k = O 1 O 2 00