Assume that Y denotes the number of bacteria per cubic centimeter in a particular liquid a that Y has a Poisson distribution with parameter 2. Further assume that A varies fr location to location and has an Exponential distribution with parameter B, where B positive integer. If we randomly select a location, what is the expected number of bacteria cubic centimeter?

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3.3
Assume that Y denotes the number of bacteria per cubic centimeter in a particular liquid and
that Y has a Poisson distribution with parameter 2. Further assume that 2 varies from
location to location and has an Exponential distribution with parameter B, where ß is a
positive integer. If we randomly select a location, what is the expected number of bacteria per
cubic centimeter?
3.4
Let Y, and Y, have a bivariate normal distribution:
21
1.
exp 2(1-p)
– 20 ()() + ()
1.
f(V1,Y2) =
-∞ < y, < ∞,
18 < y, <,
Show that the marginal distribution of Y2 is normal with mean u, and variance of is given
by:
205
fV2) =
Transcribed Image Text:3.3 Assume that Y denotes the number of bacteria per cubic centimeter in a particular liquid and that Y has a Poisson distribution with parameter 2. Further assume that 2 varies from location to location and has an Exponential distribution with parameter B, where ß is a positive integer. If we randomly select a location, what is the expected number of bacteria per cubic centimeter? 3.4 Let Y, and Y, have a bivariate normal distribution: 21 1. exp 2(1-p) – 20 ()() + () 1. f(V1,Y2) = -∞ < y, < ∞, 18 < y, <, Show that the marginal distribution of Y2 is normal with mean u, and variance of is given by: 205 fV2) =
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