# Distribution question

1. Aug 13, 2012

### LagrangeEuler

If $$P(q_1,q_2)$$ is probability distribution for two random variables $$q_1,q_2$$, let us define
$$q=\frac{q_1+q_2}{2}$$

Probability distribution for q is then

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

Why?

What is label $$\langle \cdot \rangle_P$$ exactly?

2. Aug 14, 2012

### chiro

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.

3. Aug 15, 2012