Can someone please help me with this problem? Thank you in advance!
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Can someone please help me with this problem? Thank you in
advance!
3. (10 points) Let...
Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z...
Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z and W, if it suppose N, X1, X2, are independent random variables and X,, have the same distribution function, F, and a) N-1 is a geometric random variable with parameter p (P(N-k), (k 1,2,.)) b) V - 1 is a Poisson random variable with...
please help me! Thanks in advance :) 5. Let N be a Poisson random variable with...
please help me! Thanks in advance :)
5. Let N be a Poisson random variable with parameter λ Suppose ξ1S2, is a sequence of 1.1.d. random variables with mean μ and variance σ2, independent of N. Let SN-ξι 5N. Determi ne the me an and variance of Sw. 6. Let X, Y be independent random variables, each having Exponential(A) distribution. What is the conditional density function of X given that Z =
Problem 3. (Law of Large Number and Moving Average Model) Let s0, E1, E2, be a...
Problem 3. (Law of Large Number and Moving Average Model) Let s0, E1, E2, be a sequence of i.i.d. N(0,1) distributed random variable. Define a new sequence of random variables X1, X2, X3,-.. , as: | ; Xn = uEn + O€n-1; 1 Xi, answer the following ques- where and 0 are constant parameters. Define Xn _ =1 n tions: 1) Find out Var(Xn); 2) Show that X >u as n -> c0.
Let X1, X2, X3, . be a sequence of i.i.d. Uniform(0,1) random variables. Define the sequence...
Let X1, X2, X3, . be a sequence of i.i.d. Uniform(0,1) random variables. Define the sequence Yn as Ymin(X1, X2,,Xn) Prove the following convergence results independently (i.e, do not conclude the weaker convergence modes from the stronger ones). d Yn 0. a. P b.Y 0. L 0, for all r 1 Yn C. a.s d. Y 0.
Let X1, X2, X3, . be a sequence of i.i.d. Uniform(0,1) random variables. Define the sequence Yn as Ymin(X1, X2,,Xn) Prove the following...
3. (a) (5 points) Let Xi,... be a sequence of independent identically distributed random variables e...
3. (a) (5 points) Let Xi,... be a sequence of independent identically distributed random variables e of tnduqendent idente onm the interval (o, 1] and let Compute the (almost surely) limit of Yn (b) (5 points) Let X1, X2,... be independent randon variables such that Xn is a discrete random variable uniform on the set {1, 2, . . . , n + 1]. Let Yn = min(X1,X2, . . . , Xn} be the smallest value among Xj,Xn. Show...
4. Let Xi, X2,... be uncorrelated random variables, such that Xn has a uniform distribution over...
4. Let Xi, X2,... be uncorrelated random variables, such that Xn has a uniform distribution over -1/n, 1/n]. Does the sequence converge in probability? 5. Let Xi,X2 be independent random variables, such that P(X) PX--) Does the sequence X1 +X2+...+X satisfy the WLLN? Converge in probability to 0?
8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that...
8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that M. 1, that is, M, converges in probability to 1 as n o . - Show that n(1 - M.) Exp(1), that is, n(1 - M.) converges in distribution to an exponential r.v. with mean 1 as n .
8. Let X (i-1,2) be independent N(0,1) random variables. a. Find the value of c such...
8. Let X (i-1,2) be independent N(0,1) random variables. a. Find the value of c such that P ( (X1 + X2 )2/( X2 -X1)2 < c ) =.90 b. Find P(2 X1 -3 X2< 1.5) c. Find 95th percentile of the distribution of Y-2 X1 -3 X2
Can someone help me with part (c), (with detailed explanation) Suppose that Xi,.. Xn are independent...
Can someone help me with part (c), (with detailed
explanation)
Suppose that Xi,.. Xn are independent and identically distributed Bernoulli random variables, with mass function P (Xi = 1) = p and P (Xi = 0) = 1-p for some p (0,1) (a) For each fixed p є (0,1), apply the central limit theorem to obtain the asymptotic distribution of Σ.Xi, after appropriate centering and normalisation. (b) Derive the moment generating function of a Poisson(A) distribution. (c) Now suppose that...
Problem 5: 10 points Consider n independent variables, {X1, X2,... , Xn) uniformly distributed over the...
Problem 5: 10 points Consider n independent variables, {X1, X2,... , Xn) uniformly distributed over the unit interval, (0,1) Introduce two new random variables, M-max (X1, X2,..., Xn) and N -min (X1, X2,..., Xn) 1. Find the joint distribution of a pair (M,N) 2. Derive the CDF and density for M 3. Derive the CDF and density for N.
please help me! Thanks in advance :)
5. Let N be a Poisson random variable with parameter λ Suppose ξ1S2, is a sequence of 1.1.d. random variables with mean μ and variance σ2, independent of N. Let SN-ξι 5N. Determi ne the me an and variance of Sw. 6. Let X, Y be independent random variables, each having Exponential(A) distribution. What is the conditional density function of X given that Z =
Problem 3. (Law of Large Number and Moving Average Model) Let s0, E1, E2, be a sequence of i.i.d. N(0,1) distributed random variable. Define a new sequence of random variables X1, X2, X3,-.. , as: | ; Xn = uEn + O€n-1; 1 Xi, answer the following ques- where and 0 are constant parameters. Define Xn _ =1 n tions: 1) Find out Var(Xn); 2) Show that X >u as n -> c0.
Let X1, X2, X3, . be a sequence of i.i.d. Uniform(0,1) random variables. Define the sequence Yn as Ymin(X1, X2,,Xn) Prove the following convergence results independently (i.e, do not conclude the weaker convergence modes from the stronger ones). d Yn 0. a. P b.Y 0. L 0, for all r 1 Yn C. a.s d. Y 0.
Let X1, X2, X3, . be a sequence of i.i.d. Uniform(0,1) random variables. Define the sequence Yn as Ymin(X1, X2,,Xn) Prove the following...
3. (a) (5 points) Let Xi,... be a sequence of independent identically distributed random variables e of tnduqendent idente onm the interval (o, 1] and let Compute the (almost surely) limit of Yn (b) (5 points) Let X1, X2,... be independent randon variables such that Xn is a discrete random variable uniform on the set {1, 2, . . . , n + 1]. Let Yn = min(X1,X2, . . . , Xn} be the smallest value among Xj,Xn. Show...
4. Let Xi, X2,... be uncorrelated random variables, such that Xn has a uniform distribution over -1/n, 1/n]. Does the sequence converge in probability? 5. Let Xi,X2 be independent random variables, such that P(X) PX--) Does the sequence X1 +X2+...+X satisfy the WLLN? Converge in probability to 0?
8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that M. 1, that is, M, converges in probability to 1 as n o . - Show that n(1 - M.) Exp(1), that is, n(1 - M.) converges in distribution to an exponential r.v. with mean 1 as n .
8. Let X (i-1,2) be independent N(0,1) random variables. a. Find the value of c such that P ( (X1 + X2 )2/( X2 -X1)2 < c ) =.90 b. Find P(2 X1 -3 X2< 1.5) c. Find 95th percentile of the distribution of Y-2 X1 -3 X2
Can someone help me with part (c), (with detailed
explanation)
Suppose that Xi,.. Xn are independent and identically distributed Bernoulli random variables, with mass function P (Xi = 1) = p and P (Xi = 0) = 1-p for some p (0,1) (a) For each fixed p є (0,1), apply the central limit theorem to obtain the asymptotic distribution of Σ.Xi, after appropriate centering and normalisation. (b) Derive the moment generating function of a Poisson(A) distribution. (c) Now suppose that...
Problem 5: 10 points Consider n independent variables, {X1, X2,... , Xn) uniformly distributed over the unit interval, (0,1) Introduce two new random variables, M-max (X1, X2,..., Xn) and N -min (X1, X2,..., Xn) 1. Find the joint distribution of a pair (M,N) 2. Derive the CDF and density for M 3. Derive the CDF and density for N.
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