I was confused about the question below. Can someone help me out? (I have attached this question below.) Thank you.

The number of people who win money at a casino is modelled by a Poisson process {W(t),t Z 0} with rate it people per day. Independent of other people, and independent of WU), the winner 1' wins a random amount of M, dollars, 1' = 1,2,.... The total claims by time t, shown by YO), is 0, if W(t) : 0. However, YO) is equal to 2:31\" M,, for WU) > 0. (a) [5 marks] Find the probability that 10 winners arrive by time 6:00am provided that 7 people have already won money by 2:00am. What is the maximum possible probability for this event (maximized over F)? (b) ['7 marks] Suppose that individual wins happen with respect to the following probability dis- tribution: Dollar Amount $200 $300 $600 > $600 Probability 0.4 0.3 0.2 0.1 Find the probability that the total dollar value of the wins in one day is more than $600. Your answer will be a function of it. (c) [3 marks] Now, suppose the rate of arrival of winners is a function of time, i.e. {W(t),f Z 0} is a non-homogenuous Poisson process with the rate function Iu(t)=1++~cos(7r:t) ,120 Find the probability that 10 wirmers arrive by time 6:00am provided that 7 people have already won money by 2003311