Sam will sell car to the first person to offer at least 2000. offers on his car are independent and follow an Expo(1000) distribution.
• probability that an offer will be at least 2000?
$e^{-2000/1000} = 0.1353$
• On average, how many offers will it take until Jack gets an offer of at least 2000?
1/0.1353 = 7.39
• What is the expected amount that he will get for his car (i.e. the expected value of the first offer that’s above $2000)? (Hint: No need to do integrals for this!) >
HINT
Exponential RVs famously satisfy the memorylessness property $$ P(X>m+n\mid X> m) = P(X>n).$$