The random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the probability density function of X. Find the mean and variance of X
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The random variable X has a uniform density
a. Sketch the probability density function of X. Find the mean and variance of X .
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- The probability density of the random variable X is given by: f(x) = f(x) = 0elsewhere, find the distribution function of X. = cx 2 for 0A random variable X has the density function: f(x)= K.1/(1+x2), ?? − ∞ < x < ∞ . Determine K and the c.d.f. associated with. Evaluate the probability P(X≥ 0). Find also the mean and variance of X.The function f(x) is the probability density function, that describes the random variable travel time X. f(x) = {xe®, x>0 0, X ≤0 a.) What is the probability that the travel time is less than 2.5 hours? b.) What is the probability that the travel time is between 1 to 2.5 hours? c.) Find the mean and variance of the given probability density functionLet random variable X be the length of the side of a square. Let Y be the area of the square, i.e. Y =X?. Suppose that X has the probability density function, (3x?if 0Let's say p a real function p by: 1 P(x) = 5e x ER a. Why is the function p a probability density? b. In the sequence, X is a random variable with probability density p. Calculate P(X 2 0) ? c. Calculate the expected value of X d. Calculate the variance of XWhich of the following statements about the correlation coefficient is true? A. It is a unitless number and must always be between –1.0 and 1.0, including both B.It will be 1.0 only if and only if all the data lies perfectly on the horizontal line C. Measures the fraction of extreme values (outliers) that appear in the distribution D. It is equivalent to the proportion of times that two variables join on a straight line.A. 0.342 B. 0.215 C. 0.135 D. 0.096Homework: Let X be a random variable having the density function, Find the variance of the random variable g(X) = 4X + 3. E, -1Let X be a random variable that indicates the charging time of a battery. The probability density function is as in the picture. If the battery is known to charge in more than 2 hours, the probability that it will be less than 4 hours?The plot below shows the probability density functions (PDFS) of three continuous random variables: X, Y, and Z.and markers without ink. Assume that the box contains 17 markers: 12 that contain ink and 5 that do not contain ink. A sample of 8 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. How many different values are possible for the random variable Y? 6 Part 2 Fill in the table below to complete the probability density function. Be certain to list the values of Y in ascending order. Value of Y Probability 0.0203 1 4.Help meSEE MORE QUESTIONSRecommended 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