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- fxlx,y) = x2y is a joint probability density function over the range 0Asap within 20 minutes will definitely upvoteThe 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 | 2e-(x+2y) x 2 0, y 20 fx,y(x,y) = fx.MX.v) else Then the probability that the first transistor last for at least half hour given that the second one lasts at least half hour equals Select one: a. 0.3669 b. 0.3935 c. 0.7772 d. 0.6318 e. 0.606Suppose that X and Y have a joint probability density function given by Sce-3-5y 10 if a, y 20 fx.x(x, y) = otherwise Find the conditional probability density function fyjx=z·Determine k so thatf(x, y) = kx(x − y) for 0 < x < 1, −x < y < x0 elsewherecan serve as a joint probability density.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. 0.777210) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.Let X1, X2, . X6 be an i.i.d. random sample where each X, is a continuous random variable with probability density function f(x) = e-(-0) , x > 0 Find the probability density function for X(6).This is not a complex question.2. Let X be a continuous random variable with probability density function (pdf) 3x�� 0Let X and Y has joint probability density function AX, Y) = 16 ,0SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON