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Definite Integral prob

  1. Dec 3, 2006 #1
    Hello,

    Okay so I was given a density function:

    [tex] f(x) = 2e^(-0.25x) [/tex]

    The problem asks for the value of Pr(X < or = 3)

    I first figured out the probability density function first by let

    [tex] \int (3,0) k.25e^(-.25x) = 1 [/tex]

    And figured out that k = .45

    and continue solving my problem until i get the final answer is -.212

    So, is my solution correct? Did I misunderstand something about k?

    Thanks much!

    NN
     
  2. jcsd
  3. Dec 3, 2006 #2
    Sorry, my LaTeX code looks bad.
     
  4. Dec 4, 2006 #3

    dextercioby

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    Click this picture to see where your typing went wrong

    [tex] k\int_{0}^{\infty} e^{-0.25 x}{}dx =1 [/tex]

    I don't know about the value of k, whether it's correct or not, guess not...

    Daniel.
     
  5. Dec 4, 2006 #4

    HallsofIvy

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    What do you mean, you were "given a density function:
    [itex]f(x)= 2e^{-.25x}[/itex]"? You seem to think that you need to find a multiplier k so that the "total integral" (is that supposed to be an integral from 0 to 3?) is 1. If that were the case then you wouldn't be asked for the probability that x is between 0 and 3: it would be 1!

    Dextercioby, on the other hand, seems to think that you need to find k such that the integral from 0 to infinity is 1.

    I see that we are already told that the function is [itex]2e^{-.25x}[/itex]. That is, that the "k" is 2, but that we are not given an interval over which this is to be the probability density.
     
  6. Dec 4, 2006 #5
    Daniel, yeah thanks for the code... i meant

    [tex] k\int_{0}^{3} e^{-0.25 x}{}dx =1 [/tex]

    HallsofIvy, Uh... Thats the same word from the problem in the book... and yes, thats the integral from 0 to 3... Im not sure I know about the total integral....

    Sorry about the confusion.
     
  7. Dec 4, 2006 #6

    HallsofIvy

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    Then please state the problem exactly, word for word. So far you have told us that the density function is [tex] f(x) = 2e^{-0.25x} [/tex]
    that [tex] k\int_{0}^{3} e^{-0.25 x}{}dx =1 [/tex]
    and that the problem asks for the probability that x is less than or equal to 3. I'm afraid none of that makes much sense to me. What exacly is the probability function and over what range is it defined?
     
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