(n-1)S for the conditional 1-3) Show that the moment generating function(MGF) of distribution of2,A given X...
(п-1)S? for the conditional 1-3) Show that the moment generating function(MGF) of distribution of 2,given X is (n-1)S2 | X (1-2 -(n-l)/2 ,1 < 2 E expt Hint: Notice that g,,, is a pdf That is, 7 1- "ppxp )./ (n-1)S2 X Еl exp| t in a multi-integral form using the conditional pdf of Express X2,, given X Then try to consider the integrand as another joint pdf times a constant. Then the answer will be the constant. Hint (п-1)S?...
Only 1-3) ,X, be a random sample from N(u,0") and let X and S be sample 1. Let mean and sample variance, respectively. In order to show that X and S are independent, tollow the steps below. x - x -X, and show the joint pdf of ,X,,..., X 1-1) Use the change of variable technique is (n-1)s n-u) еxp f(X,x 2a 20 av2n Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(4, /n), and...
Only 1-3) ,X, be a random sample from N(u,0") and let X and S be sample 1. Let mean and sample variance, respectively. In order to show that X and S are independent, tollow the steps below. x - x -X, and show the joint pdf of ,X,,..., X 1-1) Use the change of variable technique is (n-1)s n-u) еxp f(X,x 2a 20 av2n Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(4, /n), and...
Only 1-6) N(4,) "x.xx be a random sample from variance, respectively. In order to show that and let X and S be sample mean and sample 1. Let and 5 are independent, tollow the steps below. 1-1) Use the change of variable technique =nx-x,- x and show the joint pdf of ,X,,X is (n-1) n- exp f(,x) 20 2a av2 Use Jacobian for n x n variable transformation 1-2) Use the fact that N(u,a n), and show that the conditional...
Only 1-4) X, be a random sample from N(4,a ), , and let X and S be sample mean and sample 1. Let variance, respectively. In Order to show that and S are independent, tollow the steps below. and show the joint pdf of X,X3,*, X 1-1) Use the change of variable technique = Nx = x - is (п-1)5? п(т-и? f(E,x,) еxp ov2x 2a2 Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(u,a n)...
Let ? have a Poisson(?) distribution. (a) Show that the moment generating function (mgf) of ? is given by ?(?) = exp[?(?? − 1)]. (b) Use the mgf found in (a) to verify that ?[?] = ? and ?[?] = ?.
A random variable X has moment generating function (MGF) Problem 1. Mx(s) = (n-0.2 + 0.2e2")2 (a) Determine what a should be. (b) Determine E[X].
(4 marks The moment generating function (mgf) of a random variable X is given by (a) Use the mgf to find the mean and variance of X (b) What is the probability that X = 2?
6. (4 marks) The moment generating function (mgf) of a random variable X is given by m(t)-e2 (a) Use the mgf to find the mean and variance of X (b) What is the probability that X-2?
The moment generating function (MGF) for a certain probability distribution is given by 2 (2 + 2) , M(t) = R. t 2 Suppose Xi, X2, are iid random variables with this distribution. Let Sn -Xi+ (a) Show that Var(X) =3/2, i = 1,2. (b) Give the MGF of Sn/v3n/2. (c) Evaluate the limit of the MGF in (b) for n → 0. The moment generating function (MGF) for a certain probability distribution is given by 2 (2 + 2)...