Question

Q.9 8 marks bought almost immediately during the year, as available on the market. The event of a house becoming available follows a Poisson Houses in Auckland they become are process with rate A = 1 house per 4 days. (a) What is the expected waiting time for a house to become available? [2 marks] (b) What is the probability that exactly 10 houses become available in one week? [2 marks (c) Bob and Alice just won a Lotto and determine to buy in Auckland. Find the probability that Bob will wait between 5 and 10 days for a house to become available, given that Alice found a house in 4 days. 2 marks (d) What is the expected value and variance for the number of houses becoming available in an hour? 2 marks

Answer 1

The above problem follows Poisson process with rate=1 and t=4 days

t4 days expested esat tina time auat lable bouse a to is given by becomme 10 Exp 11 1 4 17 312 15dayys 13 pmm Prob. of exactHy 10 houses become awailable 14 Week in one days Poiscon(x) 1 week 15 -1/4 PL e 16 T/G deuys 17 65 I29004e 18 bet" 5 410 days Ae ount ing days P(bob udt bwait bet 541 days & Atite tourd in days Today's Achievement*

r(only waiiable one nouse il be 10 d be aualable bouse coi 1リ PC 4day) 10 1 P (X=1 to14 e 11 12 (4 13 pm 1 ! 14 e 4 15 X4 16 17 055 18