Question

If the variance of a poisson variate is 3 . Find the probability that 1) P(X=0) 2) P(1<X<4 ) 3) P(X>2)
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Answer 1

Answer:

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sorry for this but I don't know

Answer 2

Answer: The answer for this question..

Step-by-step explanation: Here, variance(λ)=3

we know that from poisson distribution

p(X=x)= ( e^(−λ) λ^x )/x!

1). p(x=0)= ( e^(−λ) λ^x  )/x!

             =  ( e^(-3)(3)^0 )/0!

             =   0.0498

2). before the solving we will required the value of p(x=2) and p(x=3).

p(x=2) = ( e^(−λ) λ^x )/x!

            =  ( e^(-3)(3)^2 )/2!

            = 0.2240

p(x=3) = ( e^(−λ) λ^x )/x!

            =  ( e^(-3)(3)^3 )/3!

            = 0.2240

P(1<X<4) = p(x=2) + p(x=3)

               = 0.2240+0.2240

               = 0.4480

3). we need to find p(x=1)

p(x=1) = ( e^(−λ) λ^x )/x!

            =  ( e^(-3)(3)^1 )/1!

            = 0.1494

so put the value in equation

P(X>2) = 1-[p(x=0)+p(x=1)+p(x=2)

            = 0.0498+0.1494+0.2240

            =0.4232