MATH 2233 Lecture Notes - Lecture 17: Standard Deviation
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.!
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(b) Find the probability that at most 2 cells will be found in a 20 mo2 culture.!
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(c) Find the probability that at most 2 cells will be found in a 16 mo2 culture.!
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(d) Find the probability that at least 9 cells will be found in a 16 mo2 culture.!
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(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