It is known that 15% of US home mortgages are under water (ie, the homeowner owe

Question

It is known that 15% of US home mortgages are under water (ie, the homeowner owes more than the house is worth). Suppose 18 mortgages are randomly selected (assume independence). Let the random variable X equal the number that are under water. 4.14 In reference to question (4.13), suppose mortgages are repeatedly selected at random a) Suppose the random variable X is the mortgage that is the first to be under b) Find the probability that the 10th selected mortgage is the first that is under (c) Find the probability that the first under water mortgage occurs on or before the d) Find the probability that the first under water mortgage occurs after the 2nd (e) Given that the first mortgage is not under water, find the probability that the (f) On average, how many mortgages must be selected to get the first under water? (assume independence). water. What is the distribution of X? Be sure to state the parameter. water. 3rd selected, i.e. find P(X s3) selected, i.e. find P(X> 2) second mortgage is the first to be under water, i.e. find P(X - 2X 22).

Explanation / Answer

Solution:

a)Here X : The mortgage that is first to be under water.

Here p = 0.15 , N = Total number of occurrences

b)We have to find P(X=10)

Formula:

P(X=x) = p*(1-p)(x-1)

P(X = 10) = 0.15*(1-0.15)(10-1)

P(X = 10) = 0.0347

c)P(X<=3)

Formula:

P(X <= x ) = 1 – ( 1- p )n

P(X<=3) = 1 – ( 1 – 0.15 )3

P(X<=3) = 0.3859

d)P(X>2)

P(X>2) = P ( X >= 1 )

P ( X >= 1 ) = 1 – (1 – ((1-0.15)1)

P ( X >= 1 ) = 0.85

Finally, P(X>2) = 0.85

Done

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