MATH 2233 Lecture Notes - Lecture 17: Standard Deviation

79 views2 pages

cyanreindeer497

7 Dec 2018

School

Acadia University

Department

Mathematics and Statistics

Course

MATH 2233

Professor

Wilson Lu

For unlimited access to Class Notes, a Class+ subscription is required.

Example 1: In a certain culture the average number of typhia cells (cells that cause typhus) is 5 per 20

square micrometer (mo2). The number of typhia cells is known to follow a Poisson distribution.!

(a) Find the Poisson rate.!

(b) Find the probability that at most 2 cells will be found in a 20 mo2 culture.!

(d) Find the probability that at least 9 cells will be found in a 16 mo2 culture.!

(e) Find the expected number of cells found in a 16 mo2 culture and the variance and standard!

deviation of the number of typhia cells found.

NOV 6th

2018

POISSON DISTRIBUTION

↳X= #of times arare event Eoccurs

in acertain interval

X= Poisson rate

µaverage

•271828 pirate internal size

plx )-

-Pfx -

-D= ×

E- HK51 =p

•=IF

X =

Ego

=0.25 mo

X =#of cells found in 20 mo 'culture "

× nPoi (N)

,µ-025120 )=5

PCX =P (x:o) tP(x=I )tPCX =D

=e- s (%,

t¥,

+%) =01247 - also in Table 2.

Xn Poi flu),f- 025461=4

Pfxf 2) =02381

PH7 ,9)

=I-PC48 )

=I-0.9786 =0.0214

µ= 4

64 µ=4

,6=54--2

Unlock document

This preview shows half of the first page of the document.
Unlock all 2 pages and 3 million more documents.

Already have an account? Log in

Related Questions

You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.

(a) Derive the joint pdf of X and Y. Provide this in the form of a table

Y=0 Y=1

X=0
X=1

b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?