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Distribution question

  1. Aug 13, 2012 #1
    If [tex]P(q_1,q_2)[/tex] is probability distribution for two random variables [tex]q_1,q_2[/tex], let us define
    [tex]q=\frac{q_1+q_2}{2}[/tex]

    Probability distribution for q is then

    [tex]P'(q)=\int dq_1dq_2\delta (q-\frac{1}{2}(q_1+q_2)P(q_1,q_2)=\langle \delta (q-\frac{1}{2}(q_1+q_2) \rangle_P [/tex]

    Why?

    What is label [tex]\langle \cdot \rangle_P[/tex] exactly?
     
  2. jcsd
  3. Aug 14, 2012 #2

    chiro

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    Hey LagrangeEuler and welcome to the forums.

    The symbol refers to the expectation with respect to the random variable P. This notation is used a lot in physics when denoted the expectation of a random variable.

    You also get stuff involving the other bra-ket things like inner products and the use of operators and vector products like <a|b> and |a><b| which is known as Dirac notation.
     
  4. Aug 15, 2012 #3

    Bacle2

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