Suppose we seek to estimate θ describing a multidimensional distribution from data D, some of whose points are missing features. Consider an iterative algorithm in which the maximum likelihood value of the missing values is calculated, then assumed to be correct for the purposes of restinating θ and iterated. (a) Is this always equivalent to an Expectation-Maximization algorithm, or just a generalized Expectation-Maximization algorithm? (b) If it is an Expectation-Maximization algorithm, what is  as described by Eq. 78?

~if calls to your cell phone are a Poisson process with a constant rate lambda=2 calls per hour, what's the probability that, if you forget to turn your phone off in a 1.5 hour movie, your phone rings during that time? ~How many phone calls do you expect to get during the movie?

The arrival times of workers at a factory first-aid room satisfy a Poisson processwith an average of 2 per hour. (i) What is the probability that there is at least 1 hourbetween two arrivals at the first-aid room? (ii) What is the probability that at least 3workers visit the first-aid room during a 2-hour period?

A statistics professor finds that when he schedules an office hour at the​ 10:30 a.m. time​ slot, an average of three students arrive. Use the Poisson distribution to find the probability that in a randomly selected office hour in the​ 10:30 a.m. time slot exactly five students will arrive.

A traffic enforcer counts the number of vehicle at a specific location in the highway. In his counting, there are 400 vehicles arriving per hour. Assuming that the arrival of vehicles is Poisson distributed, estimate the probabilities of having 0, 1, 2, 3, 4, and 5 or more vehicles arriving over a 20-second time interval.

A traffic enforcer counts the nunber of vehicles at a specific locationin the highway. In his counting, there are 420 vehicles arriving in a span of 1 hour. Assuming that the arrival of vehicles is poisson distributed, estimate the probabilities of having 7 vehicles arriving over a 30-second time interval, over the next 1 minute.

The average demand on a factory store for a certain electric motor is 8 per week. When the storeman places an order for these motors, delivery takes one week. If the demand for motors has a Poisson distribution, how low can the storeman allow his stock to fall before ordering a new supply if he wants to be at least 95% sure of meeting all requirements while waiting for his new supply to arrive?

People are classified as hypertensive if their systolic bloodpressure (SBP) is higher than a specified level for their agegroup, according to the algorithm in Table 5.1.Assume SBP is normally distributed with mean andstandard deviation given in Table 5.1 for age groups 1−14and 15−44, respectively. Define a family as a group of twopeople in age group 1−14 and two people in age group15−44. A family is classified as hypertensive if at least oneadult and at least one child are hypertensive. 5.17) What proportion of 1- to 14-year-olds are hypertensive? 5.18) What proportion of 15- to 44-year-olds are hyper-tensive?

To compute a Poisson probability with your calculator, press [2nd] then [VARS] to select DISTR and scroll down to poissonpdf or poissoncdf and press [ENTER]. The syntax is poissonpdf(μ, x), where μ is the occurrence rate on the given interval, and x is the desired number of successes. For “at-most” and “at-least” problems, follow a similar idea to the binomial tutorial above. Customers enter a store according to a Poisson process at a rate of 16 per hour. (a)  How likely are we to see exactly 30 customers in a two-hour period? Hint: μ = 16 × 2 = 32 customers per two-hour period. (b)  How likely are we to see at least 24 customers in a two-hour period?

A large operator of timeshare complexes requires anyoneinterested in making a purchase to first visit thesite of interest. Historical data indicates that 20% of allpotential purchasers select a day visit, 50% choose aone-night visit, and 30% opt for a two-night visit. Inaddition, 10% of day visitors ultimately make a purchase,30% of one-night visitors buy a unit, and 20%of those visiting for two nights decide to buy. Supposea visitor is randomly selected and is found to havemade a purchase. How likely is it that this person madea day visit? A one-night visit? A two-night visit?