there are three highways in the county. the number of daily accidents that occur on these highways are poisson random variables with respective parameters . 3, . 5, and . 7 . find the expected number of accidents that will happen on any of these highways today.

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25-10-2022
Mathematics

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there are three highways in the county. the number of daily accidents that occur on these highways are poisson random variables with respective parameters . 3, . 5, and . 7 . find the expected number of accidents that will happen on any of these highways today.

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contexto1019 contexto1019 · Answer 1 · 2022-11-03T06:29:08-04:00

There are three highways in the county. the number of daily accidents that occur on these highways are poison random variables with respective parameters . 3, . 5, and . 7 The expected number of accidents that will happen on any of these highways today is 1.5

There is a theorem that we can use to find the expected value of a random variable that is a sum of other random variables as follows.

If X= X₁ + X₂ +...... +Xₓ, then E( X)= E(X₁) +E( X₂) +...... +E(Xₓ),

In this case, let X = the number of accidents that will happen on any of those highways today,

are the numbers of accidents on each highway, respectively.

Then X= X₁ + X₂ +X₃ .

Since are Poisson variates, their expected values are the parameters given, .3, .5 and .7.

So E(X₁) = .3 E( X₂) = .5 E(X₃)= .7

Thus, E(X)= 1.5

A similar Poisson random variable problem is given at

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