Decide the Random Variable Distribution Parameters and Suppo

Decide the Random Variable Distribution, Parameter(s), and Support with respect to the random variable described in each scenario.

a) The arrival times of customers at a sandwich shop occur at average rate of 1 every 5 minutes. Let C represent the number of customers arriving between 1:30 pm and 1:45 pm. (Continued from above … )

b) Knowing 6 customers arrived between 3:00 pm and 3:50 pm, let D represent the number of customers who arrived between 3:00 pm and 3:30 pm.

c) Let T represent the time between customer service calls which occur at a rate of 3 per 2 minutes.

d) Let L represent the length of time for oven-baked fish to cook, which varies evenly from 12-15 minutes.

Solution

a)

poisson distribution

parameter = average = miu = landha = 1/5

b)

exponential distribution

parameter = landha = 30 minutes

c)

poisson distribution

parameter : landha = 3/2

d)

exponential distribution

mean = 3