Question b only. Would the answer be the first one? Where f(0) = .4493 Suppose t

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Question b only.
Would the answer be the first one? Where f(0) = .4493 Suppose that a computer network of s one week, so that XPolsson 0.8), with pmf experiences failures according to a process with an average of 0.8 failures per week. Let X be the number of failures in (o.8xo, 1,2,.. , otherwise Recall that the expected value and variance of a Poisson random variable both equal a) Use rpois in R to simulate 10,000 values of X. Approximately what proportion of your simulated X values are greater than 0? O 0.55 O 0.25 O 0.70 O 0.85 b) Let Y be the number of man-hours required to fix any fallures in a week, defined as tollows What is the pmf of Y 0.4493 , y-0 0.5032, y-1 or 2 O f(y)- 0.0474 , y 2 , otherwise 0.6201 , =0 0.3009 , y " 1 or 2 0.0730 , y >2 rcy)- O otherwise

Explanation / Answer

for f(y=0)=f(x=0) =e-0.8*(0.8)0/0! =0.4493

f(y=1)=f(x=1)+f(x=2)=e-0.8*(0.8)1/1!+e-0.8*(0.8)2/2!=0.5032

f(y=2)=1-f(y=0)-f(y=1)=0.0474

( it seems first one is correct ; can you tell me if there are only 3 options avaible or is there any fourth option as well)

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