Let X and Y be continuous random variables with a joint probability density function (pdf) of the form f(x,y) = {k(x+y), 0≤x≤ysl 0, elsewhere Find: a) Show that the value of k = 2 so that f(x, y) is a joint pdf. b) the marginal of X and Y. c) the joint cumulative density function (CDF), F(x, y).
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- Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.Let X1 and X2 be two continuous random variableshaving the joint probability density f(x1, x2) = 4x1x2 for 0 < x1 < 1, 0 < x2 < 10 elsewhereFind the joint probability density of Y1 = X21 and Y2 = X1X2.Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.
- Let X,Y be two random variables with joint probability density function f(x, y) =0< XThe random variable Y has probability density function f(V) = k(y + y³), 0 2. Hence find PG < Y <). iii) Find the variance of Y.The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772Let X and Y continuous random variable with joint pdf fx,y) = 24xy, for 0Let X and Y be continuous random variables with joint distribution function, F (x,y). Let g (X,Y) and h (X,Y) be functions of X and Y. PROVE Var(a + X) = Var (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 X and Y be two continuous random variables hav-ing the joint probability density f(x, y) = 24xy for 0 < x < 1, 0 < y < 1, x + y < 10 elsewhere Find the joint probability density of Z = X + Y andW = X.Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere } What is the joint CDF of X and Y?Let X be a random variable with density function - 1< x < 2, fn) = fx*/3, f(x) = 0, elsewhere. Find the expected value and the covariance of g(X) = 4X + 3.SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,