Cumulative distribution function - poisson distribution, Civil Engineering

Assignment Help:

Cumulative distribution function - Poisson distribution:

Find the cdf of Y = X1, + X2 where XI and X2 independently follow Poisson distribution with parameters λl and λ2 respectively.

Solution:

The cdf of Y is

F(y) =P(Y≤ y) =P (X1 + X2 ≤ y)

= ∑ ∑ e - λ1 λ1 x1/x1!  e- λ2 λ2x2

x1+x2 ≤  y

The summation is taken over all integer values of ( xl, x2 ) satisfying xl ≥ 0, x2 ≥ 0, x1 + x2 ≤ y . Making the substitution r = xl + x2, x1 = x We have xl = x, x2, = r-x.

Thus, region of summation in terms of r, x is all integers (x, r ) satisfying

x ≥ 0 , r - x ≥ 0, r ≤ y

or

0 ≤ x ≤ r ≤ y

Writing the summation in terms oi r and x, rearranging the terms, we have

2384_Cumulative distribution function - Poisson distribution.png

where λ = λ l + λ2 . The final expression of F (y) is the cdf of Poisson distribution with parameter λ. Hence Y also follows a Poisson distribution with parameter λ.


Related Discussions:- Cumulative distribution function - poisson distribution

Cargo handling facilities, Cargo Handling Facilities: All water transp...

Cargo Handling Facilities: All water transport terminals require cargo handling facilities. Cranes of various sizes are used. In docks, traveling cranes are popular (Figure).

Key reasons for conducting pull-out tests, Question What are key reason...

Question What are key reasons for conducting pull-out tests for soil nails ? Answer There are largely four bases for this examination- (i) To verify and verify bo

Construction management, pert disadvantages of software support, datacolle...

pert disadvantages of software support, datacollection , interpretation of results issues

Design a 10 unit rapid sand filter system, Design a 10 unit rapid sand filt...

Design a 10 unit rapid sand filter system for a flow of 6.3 MGD with a filtration rate of 2 gpm/sq ft. and an L: W ratio of 1.3.   Design flow (Q) = 6.3 MGD = 6.3x106 gpd =

Which type of pile cap transfers loads equally to piles, Q. Which type of p...

Q. Which type of pile cap transfers loads equally to piles, flexible pile cap orrigid pile cap? Loads from columns transferring to pile cap persuade tensile forces at the bott

Prismatic compass, Figure, working,principle of prismatic compass

Figure, working,principle of prismatic compass

Calculate surface loading rate for each clarifier, A wastewater plant is op...

A wastewater plant is operating at 10MGD with a suspended solids concentration of 200mg/L. It has 6 clarifiers operating in parallel. Each clarifier is 40 foot in diameter and 10 f

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd