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- e) The density function of a certain random variable X is given by xa-'(1– x)®-1 f(x) = {B(a,0) 0, if 0 0. i) Derive the expected value of X. ii) Derive the variance of X.The density function of two random variables X and Y is ,-2(x+y) fx,r (x, y) =u(x)u(y)4e¯¾x*y) X,Y Find the mean value of the function e-*+),Suppose that the random variable X has the probability density function c(1- - x2) for - 1< x <1 f(x) = { elsewhere What is the variance of X A 1/3 1/5 c) 1/2 1/4
- 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?Let X be a continuous random variable with PDF (2e*,0 /3).Let p(x) = cx^2 for the integers 1, 2, and 3 and 0 otherwise. What value must c be in order for p(x) to be a legitimate probability mass function?
- The probability density of the random variable Z isgiven by f(z) = kze−z2for z > 00 for z F 0Find k and draw the graph of this probability density.The 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 Xi be arandom sample from U(0,1)prove that Xn’ convarges in probability to 0.50
- A random variable X has the probability density function as f(x) = Ax(9-X2) 0 ≤ x ≤ 3 = 0 otherwise Find the value of A, the mean and the standard deviation of X.let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.
