Question

3.48 An apartment seeker in Manhattan estimates that 10% of the available apartments in her price range are in acceptable condition. Furthermore, she has time to look at only one apartment every weekend. a. How many weeks should this person expect to spend for apartment hunting? b. What is the probability that she will find an acceptable apartment in the first two weekends that she looks? c. What is the probability that it will take more than 4 months (17 weeks) to find an acceptable apartment?

Answer 1

Solution: Given loyd the available aponiments in her price P=0:10 There is a time only one aponiment every weefend Let x be the nod avers the perison Excepts to Spend for apartment and X follows the geometoric distribution a) E(X)= E *P(x=1) = 8 299. = P Ë 1921 =P (161-212) = P1P² 2 121 2-1 - P b) = '0.1 E(X) = 10 probabilily for first two weekends. P(x+1)+P(x=2) = 2'"'p +22 - P+2P -0.10+ (0.90)(0-10) 20.19 - P(x-1)+PCX=2)-0.19.

c) The porobobility take more than a months C17 Months) to find the acceptable apartment. P(X>17) - 1-PCX417) al-(0-93499(0-10) 31-0-8332 -0.1668 s P(X217) -0.1668