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A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let Y, denote the number of times exit i is chosen in successive runnings. For the following, assume that the rat chooses an exit at random on each run. (a) Find the probability that n = 7 runs result in Y₁ = 4, Y₂ = 2, and Y3 = 1. (Round your answer to four decimal places.) (b) For general n, find E(Y₁) and V(Y₁). E(Y₂) = V(Y₂) = (c) Find Cov(Y2, Y3) for general n. Cov(Y 2, Y 3) = (d) To check for the rat's preference between exits and 3, we may look at Y₂ - Y3. Find E(Y₂Y3) and V(Y2 - Y3) for general n. E(Y₂ - Y3) = V(Y2Y3) =

A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let Y, denote the number of times exit i is chosen in successive runnings. For the following, assume that the rat chooses an exit at random on each run. (a) Find the probability that n = 7 runs result in Y₁ = 4, Y₂ = 2, and Y3 = 1. (Round your answer to four decimal places.) (b) For general n, find E(Y₁) and V(Y₁). E(Y₂) = V(Y₂) = (c) Find Cov(Y2, Y3) for general n. Cov(Y 2, Y 3) = (d) To check for the rat's preference between exits and 3, we may look at Y₂ - Y3. Find E(Y₂Y3) and V(Y2 - Y3) for general n. E(Y₂ - Y3) = V(Y2Y3) =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents a reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let Y, denote the number of times exit i is chosen in successive runnings. For the following, assume that the rat chooses an exit at random on each run. (a) Find the probability that n = 7 runs result in Y₁ (b) For general n, find E(Y₁) and V(Y₁). E(Y₁) V(Y₁) = = (c) Find Cov(Y₂, Y3) for general n. Cov(Y2, Y3) = = = 4, Y₂ = 2, and Y3 2 (d) To check for the rat's preference between exits 2 and 3, we may look at Y₂ - Y3. Find E(Y₂ − Y3) and V(Y₂ - Y3) for general n. E(Y₂ - Y3) V(Y₂Y3) = = 1. (Round your answer to four decimal places.)
Transcribed Image Text:A learning experiment requires a rat to run a maze (a network of pathways) until it locates one of three possible exits. Exit 1 presents a reward of food, but exits 2 and 3 do not. (If the rat eventually selects exit 1 almost every time, learning may have taken place.) Let Y, denote the number of times exit i is chosen in successive runnings. For the following, assume that the rat chooses an exit at random on each run. (a) Find the probability that n = 7 runs result in Y₁ (b) For general n, find E(Y₁) and V(Y₁). E(Y₁) V(Y₁) = = (c) Find Cov(Y₂, Y3) for general n. Cov(Y2, Y3) = = = 4, Y₂ = 2, and Y3 2 (d) To check for the rat's preference between exits 2 and 3, we may look at Y₂ - Y3. Find E(Y₂ − Y3) and V(Y₂ - Y3) for general n. E(Y₂ - Y3) V(Y₂Y3) = = 1. (Round your answer to four decimal places.)
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