Let X and Y be two continmous random varíables with joint probability density function given by: f(x,y) = {Bxy, 0 SISYSI elsewhere Let cov(X,Y) = var(X) = and h(y) = {" (4y, 0sys1 elsewhere Then the value of var(X+ 2Y) is equal to:
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- Q3/ consider a random variable X with density function 0.125(4 + 2x) 1< x < 2 f (x) = elsewhere Find the variance for g(X) = 4X +3Let X1, X2, ..., X„ be a random sample from a Uniform(0,0 +1) population with 0 > 0, *(4)"^( +1) be the median of the random sample. X where n is an even integer. Let M Find the probability density function of the median M. Find the expected value and variance of M.Q4/ consider a random variable X with density function r6) = (4+*) { 0.5 < x < 1.5 f(x) : elsewhere Find the variance for g(X) = 3X4 + 2
- Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)Q//choose the correct answer 1-Let X have the density f(x) = 2x , 0 ≤x≤ 1 and f(x)=0 otherwise. the variance of the random variable Y=-2X +3. (a) 2/3 (b) 5/3 (e) 7/5 (d) 2/9Suppose that X is a random variable with density and suppose that ?=e(-4X) Determine ?(?)
- If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!Q4/ consider a random variable X with density function (4 + x) 0.5The joint probability density function of two random variables X and Y is given by f(x, y) = Ja (2x + y?) 0 3)Find the expected value and variance of the random variableX whose density function is f(x) = 1/(2(x)^0.5), 1 ≤ x ≤ 4.Find the mean of the random variable X with PDF S 3x² _if 0Prove that for the binomial population with density function f (x, p) ="C, p`q" - ', x = 1 , 2,...n. 21. the maximum likelihood estiator for p is . Find its variance.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,