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A discrete random variable X can only take the values -1, 0 and 1. The probabilities of this are P(X = -1) - p, P(X = 1) = p and therefore P(X = 0) = 1 - 2p. Here p is an unknown parameter that we want to estimate. We take a random sample X1, X2, .., Xn and consider two different estimators T1 and T2 for p: #(X; = 1) #(\X;| = 1) %3D en T, = n 2n Here # counts the number of elements, so T2 is the number of random variables that resulted in 1 or -1, divided by 2n. • Calculate the expected mean squared error (MSE) of T2 if p=0.3 and n=200. Give an exact answer. (Correct answer: 3/10000)

A discrete random variable X can only take the values -1, 0 and 1. The probabilities of this are P(X = -1) - p, P(X = 1) = p and therefore P(X = 0) = 1 - 2p. Here p is an unknown parameter that we want to estimate. We take a random sample X1, X2, .., Xn and consider two different estimators T1 and T2 for p: #(X; = 1) #(\X;| = 1) %3D en T, = n 2n Here # counts the number of elements, so T2 is the number of random variables that resulted in 1 or -1, divided by 2n. • Calculate the expected mean squared error (MSE) of T2 if p=0.3 and n=200. Give an exact answer. (Correct answer: 3/10000)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A discrete random variable X can only take the values -1, 0 and 1. The probabilities of this are P(X = -1) - p, P(X = 1) = p and therefore P(X = 0) = 1 - 2p. Here p is an unknown parameter that we want to estimate. We take a random sample X1, X2, .., Xn and consider two different estimators T1 and T2 for p: #(X; = 1) #(\X;| = 1) %3D en T, = n 2n Here # counts the number of elements, so T2 is the number of random variables that resulted in 1 or -1, divided by 2n. • Calculate the expected mean squared error (MSE) of T2 if p=0.3 and n=200. Give an exact answer. (Correct answer: 3/10000)
Transcribed Image Text:A discrete random variable X can only take the values -1, 0 and 1. The probabilities of this are P(X = -1) - p, P(X = 1) = p and therefore P(X = 0) = 1 - 2p. Here p is an unknown parameter that we want to estimate. We take a random sample X1, X2, .., Xn and consider two different estimators T1 and T2 for p: #(X; = 1) #(\X;| = 1) %3D en T, = n 2n Here # counts the number of elements, so T2 is the number of random variables that resulted in 1 or -1, divided by 2n. • Calculate the expected mean squared error (MSE) of T2 if p=0.3 and n=200. Give an exact answer. (Correct answer: 3/10000)
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