Determine the probability density function for the following hazard
rate:
z(t) = a.exp(-bt), a> 0, b >0, t>0. please help me solve this. thanks.
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Determine the probability density function for the following hazard
rate:
z(t) = a.exp(-bt), a> 0, b >0, t>0. please help me solve this. thanks.
the probability density is the function times its complex conjugate, or at least it is in quantum mechanics :-) Just the square in your case as there are no imaginary parts. |z(t)|^2=a^2exp(-2bt) ?
And if you want to normalise it, take the integral from +inf to -inf make it equal to 1, then a is determined by this :-)
a^2*(Integral (z(t) from 0 to +inf)=[(-1/b)exp(-bt)](0, inf)=1
a^2[(-1/b)- lim(s->inf){exp(-bs)}]=1
a^2(-1/b) = 1
a^2=-b
a = i(sqrt b)
Oops maybe I did something wrong?