Quiz questions

Consider the following situations one might wish to model when considering a website which sells flights. For each, decide which standard random variable distribution best models the described situation.
(A): Bernoulli (B): Discrete uniform (C): Binomial (D): Geometric (E): Poisson

1. 1.

   Number of visits The number of visits to the site in an hour.

2. 2.

   Indicator An indicator variable of whether a particular visitor to the site purchased a flight.

3. 3.

   Number of sales The number of flights sold in the first 100 visits to the site.  
   

4. 4.

   Simulate Poisson random variables Set the random seed to 123 and then use rpois to simulate 100 realisation from a Poisson distribution with rate parameter $\lambda =0.5$. What is the sum of the resulting variables?
   (A) 51, (B) 53, (C) 49, (D) 42, (E) 47

5. 5.

   Binomial probability Let $X\sim \mathrm{Bin}(15,0.4)$. Find $\mathrm{P}(4\le X\le 10)$.
   (A) 0.90015, (B) 0.77337, (C) 0.15126, (D) 4.8790, (E) 0.99065