Suppose that X and Y have a joint probability density function given by ce-3z-5y fxy(x, y) = if x, y 20 otherwise Find the marginal probability density function fx and state the name of the distribution of X.
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- Let X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.Suppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.
- 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 X₁, X2, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = (0, -, if 0Let 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).The lifetime of a machine part has a continuous distribution on the interval (0,45) months with probability density function f, where f(x) is proportional to (4+x)-2. Find the probability that the lifetime of the machine part is less than 7 months.The random variable X has probability density function 3, 1< a < 2 f(x) = otherwise. Calculate Var(4X +7).The joint density function of two continuous random variables X and Y is fxy(x, y) = (2x+y) if 2fxlx,y) = x2y is a joint probability density function over the range 0Let X be a point randomly chosen on a stick of length 1 with a uniform distribution. Let Y be a point chosen between 0 and X on this stick with a uniform distribution. Y X 1 Find the conditional probability density function (and the range) of X given Y = y. Please provide the solution step by step.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.SEE 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