Two people plan to meet to go to the bar. Each of them arrives at a time uniformly distributed between midnight and 1am and independently of the other. Denote (respectively ) the random variable representing the arrival time of the first person (respectively, the second). The joint probability distribution is given by:

(a)Find the probability that the first person is waiting for his friend for more than 10 minutes.

(b)Determine the marginal probability density functions of and . Check that thery are indeed probability density functions.

What I did so far is

Then I use formula

And the formula

But I end up , there for, the probability is no longer less than 1.

I really don't know what to do now, I thought I got the right formulae, can anyone help me please. It is same for part (b), I kind of get something, use formulae, but as question required, when I check my answer, I realised the integration of density functions don't give me 1, which means I must be wrong.

Please help me. Thanks a lot.