8. Let Y have density function y <0 f(y) cVye u y 2 0 Find the value of c that makes f(y) a density function. What are mean and variance of Y?
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![8. Let Y have density function
f(u) =
Vje u/2
Y <0
y 2 0
Find the value of c that makes f(y) a density function. What are mean and
variance of Y?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7246cbf-04e7-4dcf-91f4-884772600031%2Fa34ed197-1def-47f3-8744-3141691d975d%2Fa1uz9rw_processed.jpeg&w=3840&q=75)
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- Consider the random variable X with PDFf(x) = e−x / (1 + e−x)2 , x ∈ R.Find the density function of Y = 1/ (1 + e−X)1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.5 Y has a density function = f(y) = = 0 Find the mean and variance of Y. (Round your answers to four decimal places.) E(Y) V(Y) +y, 0≤ y ≤ 1, elsewhere.
- QI Since h(t) = 1+t 1>0 i. The survival function is given by? ii. Probability density function is given by iii. The mean time to failure(MTTF) of the component is given byThe normal probability density function g(x) = ov2n Where u = mean, o = standard deviation, n = 3.14159, e 2.71828 Let's study a special case where u = 0 and o = 1, which indicates a standard normal probability density function. For simplicity, we scale the function so as to remove the factor 1/(ov2n). Now, we have a new function f(x) f(x) = e (a) Find f'(x) and show the intervals of increase or decrease for f. (b) Find the extreme value of f. (c) Find the intervals of concavity and the inflection points. (d) Sketch the graph of f and point out the extremum value and inflection points.Şe x² f(x)=cis a probability density function? 0.111 (2 c) 0.5 /The value of the constant, which makes the function 3 >> 00w father 0.321 (
- Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 0Let X have a gamma distribution with pdf 1 f(x) Γ(α)βα What is the probability density function of Y = ex? ·xα-¹e-x/B, 0 0, ß > 0"Medians, etc problem." Suppose X has density x−2 for x ≥ 1. Find the density function for Y = X2.he length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the density function. Find the mean and variance of the random variable Y.(Continuous random variable) Impurities in the batch of the final product of a chemical process often reflect a serious problem. From a considerable amount of data collected at the plant it is known that the proportion of impurities (Y) in a batch has a density function given by: = {10(1-y)⁹ f(y): 0 ≤ y ≤ 1 en otro caso The lot is considered unsaleable, and therefore, is not acceptable if the percentage of impurities is higher than 60%. a. Verify that the above function is indeed a probability density function. b. Calculate the probability of rejecting a lot due to impurities. c. Calculate the expected value of impurities in the batch. d. Assume that the lot sells for $792 and you have to pay operating expenses of $50 for the lot. Calculate the expected profit. e. Calculate the standard deviation of the impurities in the lot and the profit.The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8SEE 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