A continuous random variable that can assume values between X = 2 and X = 5 has a density function given by fy (x) = K (1 +x). Find p (3 < X < 4)
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- 6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1], and f(x,y)=0,elsewhere. Find the expected value of the random variable Z = 10X+14Y.1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.
- 1) Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the estimator of moments for the parameter θ.1)Let x and y be two continuous random variables whose function is the probability density joint is given by : a)Draw the relationship between the variables x and y on the Cartesian axes .b)Calculate the marginal pdfs px(X)and py(Y).c)Are the v.a.s x and y independent ?4. A continuous random variable x that can assume value between x = 2 and x = 5 has a density function given by f(x) = 2/27 (1 + x). Find a) P (x < 4) and b) P (3 < x < 4)