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The number of defaults in one year within a certain portfolio of bonds is found to be a Poisson random variable

with parameter λ = 7 (i.e., the portfolio has an expectation of 7 defaults per year).

(a) Find the probability that the bond portfolio will have fewer than 3 defaults during the upcoming year.

(b) Describe the distribution of the continuous random variable representing the time between successive defaults.

(c) Find the expected time between successive defaults.

(d) Calculate the probability of there being less than 6 months between two successive defaults.

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