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Confusing Problem

  1. Apr 18, 2006 #1
    Let X be the sin of the angle theta in radians chosen uniformly from (-pi/2,pi/2). Find the mean and variance of X. HINT: X = sin(theta). Specify the support of X and check to see if your result describes a p.d.f.

    Anyone got any idea's? I managed to solve the majority of other problems and don't even know where to begin this one. Thanks for any help.
     
  2. jcsd
  3. Apr 18, 2006 #2

    HallsofIvy

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    Since the sine of any angle is between -1 and 1 the "support of X" is
    [-1,1]. The integral of 1 from [itex]-2\pi[/itex] to [itex]2\pi[/itex] is [itex]4\pi[/itex] so the "uniform distribution" density is [itex]\frac{1}{4\pi} [/itex]. The mean value of X will, of course, be
    [tex]\int_{-1}^1X P(X)dX= \frac{1}{4\pi} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}sin(\theta)cos(\theta)d\theta[/tex].
     
  4. Apr 18, 2006 #3
    First, i'd like to thank you for your response. I understand everything you said except what I left in quotes. Why did you integrate 1 from -2pi to 2pi? Other than that, I already had the support being [-1,1] and I know how to find mean and variance when given some P(X).
     
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