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Math Help - [SOLVED] pdf, mean and variance

  1. #1
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    [SOLVED] pdf, mean and variance

    Let X denote the number of alpha particles emitted by barium-133 and observed by a Geiger counter in a fixed position. Assume X has a Poisson distribution and \lambda=14.7 is the mean number of counts per second. Let W denote the waiting time to observe 100 counts. There are 25 independent observations that I organized:
    .....Frequency...... Frequency
    5.3..... 1.... ....6.9..... 2
    5.4..... 1.... ....7.0..... 1
    5.7..... 1.... ....7.1......2
    5.9..... 1.........7.2......1
    6.1..... 1........ 7.3..... 2
    6.3..... 2........ 7.4..... 1
    6.4..... 1........ 7.5..... 1
    6.5..... 1........ 7.6..... 3
    6.7..... 3

    a) Give the p.d.f., mean and variance of W
    b) Calculate the sample mean and sample variance of the 25 observations
    c) Use the relative frequency of event { {W\le6.6}} to approximate P(W\le6.6)

    For part b, I got a mean of 6.74 and variance of 0.4432. For part c, I got probability of 3.6. I can't figure out how to find the pdf for part a. I hope someone can help me. Thank you in advance.
    Last edited by antman; April 27th 2009 at 09:48 AM.
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  2. #2
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    I figured this one out! Thanks.
    Last edited by antman; April 27th 2009 at 10:32 AM.
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