using moment generting function, please write all steps 2. Problem 2: Let Xi - Bin(nı, )...
2. Let X1 and X2 be independent Poisson random variables with parameters λ1 and A2. Show that for every n 21, the conditional distribution of X1, given Xi X2n, is binomial, and find the parameters of this binomial distribution
9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c) Sn=X1+X2 + . . . + Xn. (d) An -Sn/n 9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c)...
The moment generating function ф(t) of random variable X is defined for all values of t by et*p(x), if X is discrete e f (x)dx, if X is continus (a) Find the moment generating function of a Binomial random variable X with parameters n (the total number of trials) and p (the probability of success). (b) If X and Y are independent Binomial random variables with parameters (n1 p) and (n2, p), respectively, then what is the distribution of X...
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...
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)...
Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b) Calculate the conditional distribution of Xi given Y-n for n 2 0. Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b)...
4. Let T = min(Xi, X2,Xy), where each Xi~Weibull(8,a) and X1, X2, X3 are independent (component lifetimes). Show that T also has a Weibull distribution exactly with some shape and scale parameters. (This is so-called "weakest-link model" Hint: find the reliability function of T.)
4. Let T = min(Xi, X2,Xy), where each Xi~Weibull(8,a) and X1, X2, X3 are independent (component lifetimes). Show that T also has a Weibull distribution exactly with some shape and scale parameters. (This is so-called "weakest-link model" Hint: find the reliability function of T.)
Let Xi=I(treatment for ith patient is successful).Then Pr(Xi=1|P=p)=p. Suppose that conditionally P=p, X1,X2,...Xn are independent and X=sum of Xi (x from 1 to n). Suppose P~U(0,1) (uniform distribution), want to find the EX. Could you please show me the steps of this question? Thank you so much!
I. Let X be a random sample from an exponential distribution with unknown rate parameter θ and p.d.f (a) Find the probability of X> 2. (b) Find the moment generating function of X, its mean and variance. (c) Show that if X1 and X2 are two independent random variables with exponential distribution with rate parameter θ, then Y = X1 + 2 is a random variable with a gamma distribution and determine its parameters (you can use the moment generating...