Let X be a continuous random variable with the following probability density function: f(x) = {k(6x + 2x³) 0 Find the value of k. 0≤x≤B otherwise
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![Question 1: Continuous random variables
Let X be a continuous random variable with
the following probability density function:
f(x) = {k(6x + 2x³)
0
Find the value of k.
0≤x≤B
otherwise](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb54265dd-1ffe-4eee-a1b2-a4806499bd0d%2F2f0dc3eb-468e-45a1-9f75-8c895c28af29%2F1tzfbdf_processed.jpeg&w=3840&q=75)
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- The annual rainfall in a certain country varies from 0 to 9 inches and is a random variable with probability density function defined by f(x): - 9.5 x 45 Find the following probabilities for the annual rainfall in a randomly selected year. Round your answers to 4 decimal places as needed. What is the probability that the annual rainfall is greater than 3 inches per year? What is the probability that the annual rainfall is less than 2 inches per year? What is the probability that the annual rainfall is between 2 and 4 inches per year?Let X be a random variable with density function f(x) = { k(1-x²), if 0≤x≤ 1; otherwise. Find k, together with the expectation and the variance of the random variable Y defined as Y = 3X - 1. fandWhich of the following functions are allowable as a probability density function for some continuous random variable? 0 A B D E F A: f₁(x) = C: f3(x) = {8² √3x² −1≤x≤0 else 10 I² x > 10 x < 10 E: f5(x) = 1- B: f₂(x) = D: f4(x) = x² −1 < x < 1 else {50 [5(1-x²)4 0≤x≤ 1 else (8x² - 6x +1) 0≤x≤1 else F: Neither
- The probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)Let X be a random variable with probability density function [ a + bx², 0Suppose that a random variable X has the following probability density function. SC(36-x²) 0 ≤ x ≤ 6 otherwise f(x) = {C (² Find the expected value of X. (You will need to find the value of the constant C so that f is a pdf.)Suppose an industry produced a particular type of metal mixture up to 1 ton a day. Due to technical difficulties or system breakdowns, the actual amount produced by the industry is Y, a random variable which has the following Probability density function: f(y) = √2y 0(Continuous random variable) In a city, the daily electricity consumption (millions of kWh) is a random variable whose probability density is: f(x) - ਵਿਆ = 0 x xe 3 six>0 six<0 The city's electric power plant has a daily capacity of 12 million kWh. a. Verify that the given function is a probability density function. b. Calculate the probability that the power plant cannot meet the demand for electric power.Let X be a random variable with probability density function, What is the value of c? f(x) = cx(5-x) for 0≤x≤ 5 0 otherwise O 7/28 O 6/125 O 8/81 Does not existLet X be a random variable with probability density function f(x) = x/8, where x = 1, 2 and 5; 0, otherwise. Find the expected value of x.Let X be a continuous random variable with probability density function xe-X x20 fxlx) = 0 otherwise The value of a Select one: a. can be any positive real number b. must be 1 c. can be any real number d. can be any positive integerIf X is the continuous random variable whose probability density function, Find P(X25) for 0≤x≤ 4 f(x) otherwise 0 O 1 -1 Do not existRecommended 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