Find P(X < x + 1|X > x).
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A: Since you have asked multiple questions in a single request, we would be answering only first…
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- Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...kSnowfall for a location is found to be uniformly distributed between 70” and 150”. What is the probability that a given year will have more than 120” of snow? What is the probability that the snowfall will be between 90″ and 100″?Move to Archive x 0.3e If 1-.7et is the mgf of a well known function. It is Geometric mgf i) Its name is ii) The mean of this distribution = iii) P(x = 4) = iv) The variance of this distribution is
- My Find the standard deviation of the discret probability dist x P(x) xp(x)) (x-M)² | (x-mipul 2 σ = √(x-M)² pxx) ટે О 0.21 10*0.21=0 /10-112 =. M= Exp(x) 1 0.30 1*0.3 = 0.3 2 0=49 EXP(X) =M6) (13 points) The random variable X has the following probability density function: x 1x(x)=2 0, for 0number 6If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!Q. 1 (i) Find moment generating functions (mgf) of the following probability distributions. (ii) Using mgf found in (i) above, find mean and variance. (i) fx(x;n,p) = {x)p*q"=*;_x= 0,1,2,-, n, 0; е. w. (e-^ax. x = 0,1,2,, (ii) fx(x; 2) = 0; x! е. W. 1 ( ii) fx (x; α, β) : r(a)ga x“-te¬x/B; 0 < x <∞ (iv) fx(x; ß) = e-x/B;0 < x< ∞ 1 (x-µ)²] (v) fx(x; µ, o) = To VER exp[- ;-00 < x< ∞ 2σ2 1 ( vi) fK (x; α, β) B(a,f) *"-(1 – x)*-1; 0 < x < 1 %3D Г(а)Г(В) where B(a,ß) = r(a+B) (vii) F<(x, a, f) = x«-lexp[-;)"]:0A random variable X has the distribution B(12, p). (a) Given that p = 0.25 find (i) P(X 7)Derive the variance of the Student's t distribution using the definition Var (x) = ELX2] - EX)² .The probability distribution of the discrete random variable X is Find the mean and variance of XSuppose you have a joint distribution of x and y where • x has population mean ug and population variance o? • y has population mean ly and population variance o, and the population covariance between them is Ery. The population Pearson correlation is then given by Ery OxJy We collect n pairs of data, (X;, Yi), i = 1,.. , n. Each pair is an independent draw from this distribution. (a) Suppose we estimate our population covariance with n 1 (x; – Ha)(yi – µy). i=1 Is this an unbiased estimator of the population covariance? Show why or why not. (b) Suppose we estimate our correlation with (xi – Ha)(Yi – Hy) - n i=1 Ox0y Is this an unbiased estimator of the population correlation? Show why or why not. =WISEE 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