Suppose that, during weekdays, patients arrive at the emergency room at Hospital H according to a Poisson process with rate λ patients per day. During weekends, the rate increases to 2λ per day. The manager has observed that the number of patients that arrive each day does not depend on what happens during the other days, and the manager also observed that 180 customers arrived during the past week.

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Let X be the number of patients that arrive in a week. What is the density function of X? Write down the likelihood function, L(A; 180) and the range of values of A ( using the previous density function). What is the maximum likelihood estimate X? |ь) In general, if the manager observes X patients per week, what is the c) maximum likelihood estimator of A in terms of X? d) Let Å be the maximum likelihood estimator of A. Find E(A), Var(A) and Var(A). Let X be the number of patients that arrive in a week. What is the density function of X? Write down the likelihood function, L(A; 180) and the range of values of A ( using the previous density function). What is the maximum likelihood estimate X? |ь) In general, if the manager observes X patients per week, what is the c) maximum likelihood estimator of A in terms of X? d) Let Å be the maximum likelihood estimator of A. Find E(A), Var(A) and Var(A).