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- If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?Suppose the random variable y is a function of several independent random variables, say x1,x2,...,xn. On first order approximation, which of the following is TRUE in general?If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y =X1 + 2X2 + X3 is not a sufficient estimator of θ. (Hint:Consider special values of X1, X2, and X3.)
- A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?Suppose that Z1, Z2, . . . , Zn are statistically independent random variables. Define Y as the sum of squares of these random variablesSuppose X and Y are random variables with E[XY ] = 6, E[Y ] = 4 and E[X] = 5 Find Cov(X; Y )
- For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to 2. What is P{X = 1.5 or X = 0.4}?Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]