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Poisson distribution

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  • secretliker's Avatar
    174 posts since Dec '06
    • Just part (a), I think my answer key is wrong.

      In the manufacture of glass panels, small bubbles occur at random at an average of 1 bubble in every glass panel. The number of bubbles detected in a panel is denoted by X and follows a Poisson distribution.

      (a) find the probability that, in a randomly chosen glass panel, there are at least three bubbles. [ans=0.0144?]

  • jiaxing2's Avatar
    15 posts since Jun '08
  • Uncertain's Avatar
    991 posts since Jan '07
    • X - Po(1)

       

      P(X >=3) = 1 - P(x=0) - P(x=1) - P(x=2)

       

      use this formula to get 0.0803 (same as jiaxing)

  • secretliker's Avatar
    174 posts since Dec '06
    • I got 0.0803 too. Thanks, now I can tell teacher the answer wrong.

      Uncertain, do you press calculator 3 times to get P(X=0), P(X=1), P(X=2)?

      Or can your calculator calculate directly P(X<=2)?

  • Uncertain's Avatar
    991 posts since Jan '07
    • Nope, cos i am a FM student last time... speed in calculation meant something to us.

      Ok enough of talking, i teach u a simple method.

      for P(x=0) + P(x=1) + P(x=2),        type e^(-1) [ 1+1+1/2] in your calculator

      In general, P(x=0) + P(x=1) + P(x=2) + .... = e^(-y) [ 1 + y + y^2/2 + ....]   , y = lumda

      anyway, ur calcuator cannot calculate P(X<=2) directly.

  • secretliker's Avatar
    174 posts since Dec '06
    • My calculator can calculate P(X<=2). Maybe last time cannot.

      You're using the formula for Poisson distribution right?

      ( e^-y ) [ (y^x) / x! ] , where y=lambda.

      It's in the formulae booklet but I seldom use it cos now everything is simplified by the GC.

  • Uncertain's Avatar
    991 posts since Jan '07
    • Originally posted by secretliker:

      My calculator can calculate P(X<=2). Maybe last time cannot.

      You're using the formula for Poisson distribution right?

      ( e^-y ) [ (y^x) / x! ] , where y=lambda.

      It's in the formulae booklet but I seldom use it cos now everything is simplified by the GC.


      haha secretliker.

       

      Let me share with u what i told my math student and what me and eagle share in common about the use of calculator.

       

      I strongly discouraged u from relying on calculator as....

       

      1) u will miss out a lot of concept when u rely on it. a classical example is the sketching of graph.... which involves differentiation, partial fraction and finding the intercepts.....

       

      2) what if ur calculator spoil and cannot be replaced? U have to re-learn all the functions (worst still some functions got several symbols and wordings).

       

      Therefore, i urge u to use calculator for PLAIN calculation and not relying on it to solve question (but for double checking is fine). 

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