2.A sports analyst decides to model baskets scored in a WNBA game as a Poisson processwith rate 4.2 per minute.(a) What distribution would you use to model the amount of time until the first score in a WNBAgame? Define any parameters you use.(b) Compute the likelihood that the first score occurs between 30-45 seconds. You may leave youranswer in terms of exponentials.(c) Suppose the analyst wants to use a x² test for goodness of fit to evaluate whether this distributionis a good model. They record the following data from 30 games:Time of First Score 0-15s 15-30s 30-45s 45-60s 60s+Count511446Using your answer from (b) what is the expected count for the 30-45s bin?(d) How many degrees of freedom are there for the test statistic in this test?

A sports analyst decides to model baskets scored in a WNBA game as a Poisson process with rate 4.2 per minute.a)The Exponential distribution is used to model the time until an event occurs in a Poisson process. The exponential distribution that can be used to model the amount of time until the first score in a WNBA game.The parameter for the exponential distribution is the rate, which in this case is 0.07 per second.b) Apply the formula for exponential distribution:The likelihood that the first score occurs between 30 to 45 seconds is 0.0796.c)The expected count for the 30 to 45s bin is 2.388.d)The formula for degree of freedom for the goodness of fit test is given below:The degrees of freedom for the test statistic in this test is 3.a) The Exponential distribution is used to model the time until an event occurs in a Poisson process. The exponential distribution that can be used to model the amount of time until the first score in a WNBA game. The parameter for the exponential distribution is the rate, which in this case is 0.07 per second.b) The likelihood that the first score occurs between 30 to 45 seconds is 0.0796.c) The expected count for the 30 to 45s bin is 2.388.d) The degrees of freedom for the test statistic in this test is 3.