The random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density function.b. Compute P(x = 1.25).
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The random variable x is known to be uniformly distributed between 1.0 and 1.5.
a. Show the graph of the probability density function.
b. Compute P(x = 1.25).
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- e Define and explain joint distribution function and joint density function of two random variables X and Y.This is Involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 17 markers: 14 that contain ink and 3 that do not contain ink. A sample of 4 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. Fill in the table below to complete the probability density function. Be certain to list the values of Y in ascending order.Suppose the probability density function for a uniform distribution ranging from 0 to 1. The mean of the random variable X for this distribution is O a. 0.50 O b. 0.75 Ос. 0.25 d. 1.00
- In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is 1 2 p(x) 0.3 0.6 0.1The table below represents the probability density function for the random variable X. Find the standard deviation of X. Round the final answer to two decimal places. x P(X = x) 1 1/4 3 1/4 4 1/22. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs 2 S (v) . else What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density а. function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: Find?(r - 1.5)) = 1 CO0
- Assume that the machine yields the item selected 90 percent of the time, and returns nothing 10 percent of the time. Three individuals attempt to use the machine. Let X be defined as the number of individuals who obtain the item selected. How many different values are possible for the random variable X? Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.Students arrive at a lecture theatre independently. Suppose the number of students arriving in an hour follows a Poisson distribution with mean 10. Let 7 (in hours) be the time required to wait for 5 students to arrive. Derive the probability density function of T.For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.5 and 3.2? f(x) = {C(1+ x) ,1For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.3 and 3.1? с (1 + х) ,1 <The table below represents the probability density function for the random variable X. Find the standard deviation of X. x P(X = x) 0 1/6 1 1/6 4 1/3 7 1/3The probability density of a random variable X is given in the figure below. 1 2. From this density, the probability that X is at least 0.78 is:Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman