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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Solve all 4 part

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.)
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman