Hi, I cannot really understand what the part a and b mean in the question below.

Can you help to explain it to me? Thx

The number of people who win money at a casino is modelled by a Poisson process {W(t),t 2 0} with rate 31 people per day. Independent of other people, and independent of W(t), the winner 1' wins a random amount of M,- dollars, i = 1,2,.... The total claims by time t, shown by Y\"), is 0, if W(t) = 0. However; Y[t) is equal to {2:9} M,, for WU) > U. (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 l $200 $300 $600 > $600 Probability l 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 y. (c) [3 marks] Now, suppose the rate of arrival of winners is a function of time, i.e. {W(t),t Z 0} is a non-homogenuous Poisson process with the rate function y(t)=1+cos(?r:t) , t20 Find the probability that 10 winners arrive by time 6:00am provided that 7 people have already won money by 2:00am