2. (Ross 3.2) Let Xi and X2 be independent geometric random variables having the same parameter...
Let X1 and X2 be independent geometric random variables with the same p. What is the PMF ofs=x, +X2? 5.15
E. Let Xi, X2, be independent random variables from a geometric distribution with parameter 0.1. Verify, whether the sequence n1,2, n+ 31 converges almost surely and if yes, find the limit.
Suppose Xi, X2,.. are independent Geometric (number of trials) random variables where ~Geometric p 1- a) It is easily shown that Xfor some constant a. Name it. a= b) According to the Borel-Cantelli Lemmas, does a.s /n In other words, will there eventually reach a point in the sequence of random variables where every X a?
Suppose Xi, X2,.. are independent Geometric (number of trials) random variables where ~Geometric p 1- a) It is easily shown that Xfor some constant...
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...
PROB 4
Let Xi and X2 be independent exponential random variables each having parameter 1 i.e. fx(x) = le-21, x > 0, (i = 1,2). Let Y1 = X1 + X2 and Y2 = ex. Find the joint p.d.f of Yi and Y2.
Suppose X1, X2,... are independent Geometric (number of trials)
random variables where Xi ~ Geometric(p = 1/i^2)
a) It is easily shown that Xn converges to a for some constant
a. Name it.
b) According to the Borel-Cantelli Lemmas, does Xn almost surely
converge to a?
Suppose Xi, X2, are independent Geometric (number of trials) random variables where x,~ Geometric(pal+) |. a) It is easily shown that Xa for some constant a. Name it. b) According to the Borel-Cantelli Lemmas,...
Let Xi and X2 be independent Poisson random variables with means λ! and λ2. (a) Find the distribution of x, + x, (b) Compute the conditional distribution of Xi given that X + X.-n
Problem 4 Let X and y be independent Poisson(A) and Poisson(A2) random variables, respectively. i. Write an expression for the PMF of Z -X + Y. i.e.. pz[n] for all possible n. ii. Write an expression for the conditional PMF of X given that Z-n, i.e.. pxjz[kn for all possible k. Which random variable has the same PMF, i.e., is this PMF that of a Bernoulli, binomial, Poisson, geometric, or uniform random variable (which assumes all possible values with equal...
Exercise 6.48. Let X1, X2, ..., Xin be independent exponential random variables, with parameter lį for Xi. Let Y be the minimum of these random variables. Show that Y ~ Exp(11 +...+ In).
4. Let Xi,X2, , Xn be n i.id. exponential random variables with parameter λ > Let X(i) < X(2) < < X(n) be their order statistics. Define Yǐ = nX(1) and Ya = (n +1 - k)(Xh) Xk-n) for 1 < k Sn. Find the joint probability density function of y, . . . , h. Are they independent? 15In