1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to solve for probability given density function

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data
    The probability density function of a random variable y is:
    f(y) = 100ye[itex]^{-10y}[/itex], if y>0
    f(y) = 0 otherwise

    What is the probability that 45y <= 10?



    2. Relevant equations
    E(y) = ∫yf(y)dy
    Var(y) = ∫(y-E(y))f(y)dy



    3. The attempt at a solution
    I solved for the expected value of y and got E(y) = 0.2
    I then got Var(y) = 0.02
    I don't think this is a normal distribution because the PDF is not a normal
    PDF. I don't know how to solve for the probability of 45y <= 10

    Any help will be greatly appreciated!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 4, 2012 #2
    Not quite sure, but maybe you do ∫f(y) dy from 0 to 10/45?
     
  4. Feb 4, 2012 #3
    I thought about that, but it just didn't seem right, after all, if one of the y's is over 10/45, the other y's can be less than that to make up for it.
     
  5. Feb 4, 2012 #4

    Curious3141

    User Avatar
    Homework Helper

    You shouldn't be worrying about what sort of distribution this represents. You're already given a pdf. Compute the cdf (cumulative distribution function). If the pdf is [itex]f(y)[/itex], the cdf is [itex]\int_{-\infty}^y f(y)dy[/itex]. Remember that from -∞ to 0, f(y) = 0, so break it up into two integrals, one from -∞ to 0 (which vanishes), and the other from 0 to y.

    Do the integration by parts and work out the definite integral in terms of y. Then it's as simple as substituting y = 10/45 into that.

    The answer I get lies between 0.6 and 0.7, if you wish to check yours.
     
  6. Feb 4, 2012 #5
    Ahh yes, I see, thank you very much. I got the same answer.
    Thanks again!
     
  7. Feb 4, 2012 #6

    Curious3141

    User Avatar
    Homework Helper

    No problemo. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to solve for probability given density function
Loading...