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Discrete/Poisson Distribution

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    A Geiger counter was set up in the physics laboratory to record the number of alpha particle emissions of carbon-14 in 0.5 second. The following are 25 observations made during 0,5 second intervals :

    4,6,11,10,10 9,9,9,4,11 11,4,8,5,7 6,4,4,7,5 10,6,12,7,13 (a) Compute the sample mean x for these data.
    (a) Compute the sample mean
    (b) Let X equal the number of particle detections in .5 second period. What (approx) distribution would you assign to X.
    (c) Compute P (X ≤ 6)
    (d) What is the expected value of X based on your model?



    2. Relevant equations

    Sample mean = Ʃ [x * f(x)]/n

    Poisson Distribution = [λx e]/x!

    3. The attempt at a solution

    a) Sample mean = 7.68
    b) λ = 7.68...?
    c) using the formula for Poisson distributions, P (X ≤ 6)=.222
    d) μ = λ= 7.68
     
  2. jcsd
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