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:

[4/3t]

=

4/3 - 1/3 = 1

giving the answer as 1. Is this right?

thanks