X -1 that the following function satisfies the properties of a joint probability mass function 0.5 y fxy(x,y) -2 1/8 -0.5-1 1/4 1 1/2 1 2 1/8 f(x, y) > and Σf(x, y) =i
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![Show that the following function satisfies the properties of a joint probability mass function.
x y
fxY(x,y)
-1
-2 1/8
-0.5 -1 1/4
0.5 1 1/2
1
2 1/8
f (x, y) >
and Σ f(x, y) =
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- 8)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the joint probability density function of the order statistics X(2), X(4), X(6) for n = 7.Let f(x) = Ce-x/1+e-2x for all x in (-infinity, infinity). If f is a probability density function for a random variable X on (-infinity, infinity), answer the following: (a) Find the value of constant C. (b) Evaluate the probability P(X<-4). Correct to four decimal places.The joint probability mass function of Xand Ylis given by p(1, 1) = 0.2 p(2, 1) = 0.1 p(3, 1) = 0.05 p(3, 2) = 0.1 Р(1,2) - 0.1 p(2, 2) = 0.05 p(2,3) 0.05 p(1, 3) = 0.1 p(3, 3) = 0.25 %3D (a) Compute the conditional mass function of Ylgiven X 2: P(Y = 1|X = 2) D %3D P(Y = 2|X 2)= P(Y 3|X = 2) (b) Are Xland Yindependent? (enter YES or NO) NO
- 1. A continuous random variable X has a probability density function (PDF) p(x) = k( 8-x^2/2) on the interval [0, 4] (a) Find k such that p(x) is a valid PDF. (b) Find P(X ≤ 1). (c) Find the mean, µ, of X. (d) Find the variance, σ 2 , of X.The joint probability mass function of X and Y is given by P(1, 1) = 0 p(2, 1) = 0.05 p(3, 1) = 0.1 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = P(Y = :2|X = 2) = P(Y = 3|X = 2) = (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X+Y> 2) = P(XY = 3) = P(> 1) = p(1,2)= 0.1 p(2, 2) = 0.3 p(3,2)= 0.05 p(1,3)= 0.05 p(2, 3) = 0.1 p(3, 3) = 0.25Find the value of k for the probability mass function 4 f(x) = k () , ) for x = 0,1,2. %3| 4 -
- сх, f(x)= 0The joint probability density function of X and Y is defined as f(r, y) = (1+2?)(1+y²) What is the probability that (X, Y) falls inside the square with vertices (0,0), (1,0), (1,1), and (0,1)? 16 O 1/2 O None of these. O 1/16function f (x, y) =15e-2x-3y a joint probability density function over the range 0Q1. Random variables X and Y have joint Probability Density Function (PDF) fxx(x, y) = {2 - 1< x < y < 1 otherwises Find rx,y and E[e*+Y].he joint probability density function of two random variables X and Y given by fxY (x, y) = c (2x +y) for 0 SxS1, 0S y S2 elsewhere Find (a) the value of C|A 9 a) The continuous random variable Xhas probability density function f (x) = 0(1– x)"-1 , 0 0 i) Find the cumulative distribution function, F(x), of X ii) Find P(0.25SEE 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