Quiz solutions for Math 103 Probability: Week 13

1. Number of visits: E, the number of events in a fixed time interval is usually well modelled by a Poisson rv.

2. Indicator: A, since indicators take values 0 or 1, and any random variable taking these values is Bernoulli.

3. Number of sales C, since there are a fixed number of trials (100) and we’re measuring the number of successes

4. Simulate Poisson random variables E
   The code to use is

   set.seed(123)

   y <- rpois(100,0.5)

   sum(y)

   which gives answer 47.

5. Binomial probability A
   One can use various forms, including:

   p <- dbinom(4:10,15,0.4)

   sum(p)

   or

   pbinom(10,15,0.4) - pbinom(3,15,0.4)

   Both give the answer 0.90015.