A continuous random variable X that can assume value between x-2 and x-5 has a density function given by 1+x f(x) = 8 a. Show that P(2
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- Suppose that X1, X2, and X3 are i.I.d random variables each with density function f(x)= {((1/4)x^3) if 0 < x < 2 { 0 otherwise Let the random variable M be the max of X1,X2, and X3. What is the E(M)?Let Xbe a continuous random variable with density f (x) = 24x-4 for x > 2. Then Var (X) is equal toLet X and Y be two continuous random variables with joint probability density [3x function given by: f(x,y)= 0Be X a random variable with density function defined by f(x) = -2², , x>0. 3 Get the moment-generating function and based on it, calculate the average and variance of X.Show that if a random variable has a uniform density with parameters α and β, the probability that it will take on a value less than α+p(β-α) is equal to p.2. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhereLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.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?A 10 A continuous random variable that can assume values between X = 2 and X = 5 has a density function given by fx (x) = K (1 +x). Find p (3 < X < 4)Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X + 25. Then what is the probability density function of Y (fy(y)). Probability TheoryIf X is a continuous random variable find the CDF and density of the function y = x/3Let 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.SEE MORE QUESTIONS
