- #1
LagrangeEuler
- 717
- 20
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?
[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?