(17) Suppose X has the following pmf: p(0) = 0:2; p(1) = 0:5; p(2) = 0:3.
Calculate E(X), E(X2), and E(X2) - E(X)2.
(17) Suppose X has the following pmf: p(0) = 0:2; p(1) = 0:5; p(2) = 0:3....
Consider the following PMF for a continus random variable f(x) = 0,25-Kx®2 Calculate K Calculate P(3<x<5) Calculate P(X <= 4) Calculate E(X) Calculate Var(X)
3. Suppose that X1, X2, X3 be i.i.d. random variables with P(Xi 0) 2/5 and P(X 1) 3/5. Find the MGFof X, + X2 + X 3.
3. Suppose that X1, X2, X3 be i.i.d. random variables with P(Xi 0) 2/5 and P(X 1) 3/5. Find the MGFof X, + X2 + X 3.
Suppose a random variable X has a pmf p(x) = [3^(x-1)] / [4^x] , x = 1, 2, ... (a) Find the moment generating function of X. (b) Give a realistic example of an experiment that this random variable can be defined from its sample space. (c) Find the mean and variance of X.
5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
Suppose that X is a discrete random variable with pmf, p(x), arn x1 and x2 be numerical values in the range of X. dCDEFGT-Let- What should be in the blank space? F(0) Fx1)
find the pmf of x, p(3/5 < x < 3), the expectation of x,
and the standard deviation of x
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Supposed the following data: 0, 2, 0, 2, 0 are observed from the distribution with pmf p(x =0;θ)= 1−θ 3 ;p(x =1;θ)= 1 3;p(x =2;θ)= 1+θ 3 ; and 0, otherwise. Find the MLE of θ. Calculate the MLE of P(X =2).
Let the probability mass function of X be given as 5. | | P(X-x) a) Find the pmf of Y2 b) Find the pmf ofY X2 0.3 0.60
Let the probability mass function of X be given as 5. | | P(X-x) a) Find the pmf of Y2 b) Find the pmf ofY X2 0.3 0.60
3. Let X1,..Xn be a sample with joint pdf (or pmf) f(x,0), 0 e 0 c R. Suppose that {f(x, 0) 0 e 0} has monotone likelihood ratio (MLR) in T(X,). Consider test function if T(xn)> c if T(xn) c if T(x)<c 0 E [0,1 and c 2 0 are constants. Prove that the power function of ¢(X,) is where non-decreasing in 0
3. Let X1,..Xn be a sample with joint pdf (or pmf) f(x,0), 0 e 0 c R....
Consider a random variable X with RX = {−1, 0, 1} and PMF P(X =
−1) = 1/4 , P(X = 0) = 1/2 , P(X = 1) = 1/4 .
a) Determine the moment-generating function (MGF) MX(t) of
X.
b) Obtain the first two derivatives of the MGF to compute E[X]
and Var(X).
Consider a random variable X with Rx = {-1,0,1} and PMF Determine the moment-generating function (MGF) Mx(t) of X b) Obtain the first two derivatives of...