(а) Find k (b) Find marginal densities of X and Y
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A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted
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- Let X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysxThe joint probability density function of two random variables X and Y is given by f(x, y) = Ja (2x + y?) 0 3)The joint probability density function of two random variables given by fxy(X.y) = x(X-y)/8, 0 < x < 2; -xc) A continuous random variable X takes values in the interval 1 < x < 3and the probability density function of x is given by: k f(x) (i) (ii) Plot the pdf of the X Show by calculation how you can determine the value of K, the expected value and the varianceA random variable X has probability density function given by if r 1 fx(x) = (a) What is the expectation E(X)? (b) What is the variance Var(X)?Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.A continuous random variable X has probability density function f given by (kx* (4-x) for 0sx54 f(x)={ elsewhere Find (a) the value of k. (b) the mean and variance of X. (c) P(lThe 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+2) x 2 0, y 20 fx,y(x,y)=| 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. 0.3935 b. 0.606 c. 0.7772 d. 0.3669 e. 0.6318Let X and Y be two continuous random variables with joint probability density (3x function given by: f (x.y)=D 0For the continuous probability function f(x) = Kx² ex when x ≥ 0 find i) k ii) mean iii) variance =(A=X) qA variable X is distributed at random between the values 0 and 4 and its probability density function is given by: f(x) = kx³ (4- x)². Find the value of k, the mean and standard deviation of the distribution.Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?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,