flies and wasps in land on your dinner plate in the manner of independent poisson with...

flies and wasps in land on your dinner plate in the manner of independent poisson with respectives lamda and meu. show that the arrivals of flying objects form a poisson process with intensity lamda + meu

Solutions

Expert Solution

Flies:

X is a Poisson Distribution with parameter

Wasps:

Y is a Poisson Distribution with parameter .

To prove:
Z = X + Y is a Poisson Distribution with parameter

Proof:

By Theorem:

If X and Y are Independent Discrete Random Variables with Probability Mass Functions p_x(x) and p_y (y), then, the Probability Mass Function of

Z = X + Y

is given by:

Using the above Theorem:

The Distribution of Z = X + Y is given by:

The above computation establishes that the sum Z of the two independent Poisson distributed random variables X and Y with mean values and also has Poisson distribution of mean .

Thus, we show that the arrivals of flying objects form aPoisson Processwith intensity .

orchestra answered 2 years ago

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