Question

Let descrete random variable X~Poisson(6). Find: Probability P(X=5) Probability P(X=2) Probability P(X<3) Probability P(X>6) μX σX

Let descrete random variable X~Poisson(6).

Find:

Probability P(X=5)

Probability P(X=2)

Probability P(X<3)

Probability P(X>6)

μX
σX

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

X ~ Poisson () = Poisson (6)

Where = 6

P(X) = e-X / X!

a)

P (X = 5) = e-6 65 / 5!

= 0.1606

b)

P( X = 2) = e-6 62 / 2!

= 0.0446

c)

P( X < 3) = P( X <= 2)

= P (X = 0) + P (X = 1) + P (X = 2)

= e-6 60 / 0! +e-6 61 / 1! +e-6 62 / 2!

= 0.0620

d)

P( X > 6) = 1 - P( X <= 6)

= 1 - [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) ]

= 1 - [ e-6 60 / 0! +e-6 61 / 1! +e-6 62 / 2! +e-6 63 / 3! +e-6 64 / 4! +e-6 65 / 5! +  e-6 66 / 6! ]

= 1 - 0.6063

= 0.3937

e)

x = = 6

f)

x = sqrt ( ) = sqrt( 6)

= 2.4495

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