Question

An Explanation is required for this assignment. Please explain the answers.

Chapter 6 Reflection: In the economic slump of the early 2000s, there was an increase is home foreclosures. Statistics from BBU Bank show their monthly foreclosure rate is now 1 loan out of every 136 loans. Last month the bank approved 300 loans. (Hint: This describes a Poisson distribution.) 1. How many foreclosures would you expect the bank to have last month? 2. What is the probability of exactly two foreclosures? 3. What is the probability of at least one foreclosure?

Answer 1

X be the number of foreclosures follows poisson distribution with probability 1/136

probability of foreclosure = 1/136

number of loan = n = 300

1) Expected number of foreclosures in last month = n*probabilty = 300*(1/136) = 2.2 ( or 2 if to be discrete )

lambda = 2

2) Probability of exactly 2 foreclosures = P[X=2] = e^(-lambda)*lambda^x / x_factorial = e(-2) * (2)^2 / 2_factorial = 0.135*4 / 2 = 0.135*2 = 0.27

3) Probability of at least 1 foreclosures = P[X>=1] = 1 - P[X=0] = 1 - e^(-lambda) = 1 - e^-2 = 1 - 0.135 = 0.865