It is known that if bacteria are grown on a maintenance board of area A, and if Y = thenumber of colonies of bacteria in a small area a selected at random from the board,then Y has a Poisson distribution with a mean alA (number of colonies on the entireboard). Suppose p = 5.5,Calculate the probability that:(a) At most 3 colonies were found in that area.(b) More than 8 colonies will be found in the area.

We want to find following probability X~Poisson(μ=5.5)

Answered: It is known that if bacteria are grown…

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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5. A quality control engineer found that the inner and outer diameters of their ball bearings, denoted respectively as X and Y, are random variables with E(X|Y = y) = 0.7 – 0.3y inches and Var(X|Y = y) = 0.0004y for all values of y. From his past experience he also knew that the mean and variance of the outer diameters were E(Y) = 0.7 inches, and Var(Y) squared inches. = 0.0001 %3D • (i) What are the conditional random variables, E(X|Y) and Var(X|Y)? • (ii) Find the mean of the inner diameters, E(X). • (ii) Find the variance of the inner diameters, Var(X).
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