Let (N1,N2,...,Nm) be distributed as Multinomial(n,p1,p2,...,pm). (a). the conditional covariance between Ni and Nj for i, j ≤ r given (N(r+1), . . . , Nm) (b). an appropriate approximation to the probability that N1 is larger than 65 when N = 100 and p1 = 0.25

Let (N1,N2,...,Nm) be distributed as Multinomial(n,p1,p2,...,pm). (a). the conditional covariance between Ni and Nj for i, j ≤ r given (N(r+1), . . . , Nm) (b). an appropriate approximation to the probability that N1 is larger than 65 when N = 100 and p1 = 0.25

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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Let (N1,N2,...,Nm) be distributed as Multinomial(n,p1,p2,...,pm).

(a). the conditional covariance between Ni and Nj for i, j ≤ r given (N(r+1), . . . , Nm)

(b). an appropriate approximation to the probability that N1 is larger than 65 when N = 100 and p1 = 0.25

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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