Probability CCDF developped to Expectation form for an exponential distribution

176 Views Asked by At

Please, can someone help me to prove this formula?

$$ P\{\,H ≥ k.R^a.(J(R)+N)\,\} = E_R\{\,exp(-k.R^a.N/q). E[ exp(-k.R^a.J(R)/q)|R]\,\}$$

With H is exponential distribution with parameter q.

P is the probability. J(R) is a function of R.

E is the expectation.

I hope that the formula is clear enough.

Many thanks in advance :)