A bus company is about to start a scheduled service between two towns. Before deciding on an appropriate timetable they do ten trial runs to see how long the journey takes. The times, in minutes, are:
89 92 98 34 98 34 98 98 34 34
95% interval for mean journey time?
R.v.s s and t have joint p.d.f f(s,t) = 6s, 0<t<s<1. I worked out their marginal densities as
fs(s) = 6s^2
ft(t) = 3-3t^2
and their conditional densities as
f(t given s) = 1/s
f(s given t) = 6s/(3-3t^2)
(a) for what range are the conditional densities valid?
(b) find (t>0.25 given that s = 0.75)
I substituted numbers into the f(t given s) = 1/s equation to get
1/s = 4/3.
Then I integrated this with respect to t, upper limit 1, lower limit 0.25:
4/3 - 1/3 = 1
giving the answer as 1. Is this right?
In that thread you define the support as 0 < s < t <1. This is NOT the same as the support defined in this thread, namely 0 < t < s < 1. The joint pdfs in each thread are therefore very different from each other.