Question

Problem 3 The time (in years) after reaching age sixty that it takes an individual to retire is approximately exponentially distributed with a mean of about five years. Suppose we randomly pick one retired individual. We are interested in the time after age sixty to retirement. In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest 0.01 . a. The time after sixty to retirement is modeled by a random variable X with X (pick one) ( distribution. b. The mean of X is Mx = C. The standard deviation of X is Ox = d. Probability that individual retired after 74 is P(X > 14) = e. Do more people retire before 65 or after 65 ? (pick one)

Answer 1

a)X~ Exp(5)   (please try Exp(0.2) if this comes wrong and reply)

b)

mean μ =

1/λ=β =

5.00

c)

standard deviation σ=

1/λ=β =

5.00

d)

P(X>14)=1-P(X<14)=1-(1-exp(-14/5))=

0.0608~ 0.06

e)

before 65 (since probability of retiring before 65 =1-exp(-5/5) =0.6321)