Let X₁, X2, ..., Xn be a random sample from a population with probability density function 4 ƒ(2) = 3²¹ √ 2²° e ¯¾‚ 0 < Find a sufficient statistic for 3. Justify your answer. 0

Don't Hand writing in solution.

13. Suppose a continuous random variable x has the probability density Sk(1+ x), 0 1.4) using distribution function, determine the probabilities that (d) x is less than 2.2 (e) between 1.4 and 1.6 (f) Calculate mean and variance for the probability density function.

2. where The random variable, X, has a probability density function (pdf), f(x), and zero otherwise. (a.) (b) x+1, f(x) = {1x, 1 81 -1/2 < x < 0 0