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Cant understand this integral(probability)

  1. Feb 17, 2010 #1
    2ngr2uo.jpg

    if we integrate by U
    then if we take steady point on U axes we
    encounter 1-v and 3-v lines
    thus making our intervals for each steady U point
    but why 0<v<1??
    there is a red point in the photo in our area in which v=3

    ??
     
  2. jcsd
  3. Feb 17, 2010 #2
    the blue line should be parallel to the horizontal axis
     
  4. Feb 17, 2010 #3
    since you are integrating in terms of u. for v between 0 and 1, du will be between the two lines mentioned. for v between 1 and 3, u will vary between the v-axis and 3-v. to check it try performing the volume integral which shows that it is indeed a probability density.
     
  5. Feb 17, 2010 #4
    no if we go by du then we go by the u axes
     
  6. Feb 17, 2010 #5

    cronxeh

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    Gold Member

    I don't understand the chicken scratch on the photo you posted. The first integral doesn't make sense. The area between 0 and v=1 and u=1 is 1/2*base*height = 1/2*1*1 = 1/2. The probability in this area is 0.

    The second shaded area has area of 1/2*3*3-1/2 = 4. The total probability in this area is 1/4*4 = 1 which is your state space.

    If you are integrating along u that means the area of a little strip is height*du, the height being delta v
     
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