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A PDF formed from a multivariate function

  1. Oct 2, 2016 #1
    1. The problem statement, all variables and given/known data
    A probability density function, ##p\left(x\right)=\int _{-a}^a\left(f\left(x,\left(a-y\right)\right)-f\left(y,ax\right)\right)dy##, can be formed from the bivariate function ##f\left(x,y\right)=y\sqrt{\left(x-2\right)^2-y}## over the domain ##[0,b]## - where ##b## is the coordinate of the x-intercept.

    (a) Determine the values of ##a## and ##b## correct to 5 decimal places
    (b) Calculate the expected value, variance and standard deviation of ##p(x)## correct to 4 decimal places
    (c) Find the percentage probability of the continuous random variable ##X## being withing ##|a|## standard deviations either side of the mean​

    2. Relevant equations
    Knowledge or probability density functions, including integral applications.

    3. The attempt at a solution
    Well I know that I need to substitute the actual values for ##f\left(x,\left(a-y\right)\right)## and ##f\left(y,ax\right)## into ##p(x)## to be able to integrate ##\int _{-a}^a\left(f\left(x,\left(a-y\right)\right)-f\left(y,ax\right)\right)dy##, and then I'd need to solve ##int_0^b p(x)dx for b and then use that to solve for a. However, when I attempt to do this on my calculator I receive and error message. Does anyone know how I could do this?
     
  2. jcsd
  3. Oct 7, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    Which error message do you get?
     
  4. Oct 9, 2016 #3
    I receive the message: "ERROR: Insufficient Memory"
     
  5. Oct 10, 2016 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Maybe you can simplify the function a bit, or use a better calculator.
     
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