Question 1: A continuous random variable Y has P(Y > 10) = 0.16 and P(5 ≤ Y ≤ 10) = 0.15. Find:

(a) P(Y < 10)
(b) P(Y < 5)
(c) P(Y = 0)

Question 2: Jenny will be receiving an antique item as a gift from her parents. She is not sure about the value of the item but she understands that she can sell the antique for $2, 000 with 0.4 probability, $200 with 0.5 probability and $20 with 0.10 probability. Would you suggest Jenny to accept $1,000 instead of receiving the antique?

Question 3: The time between arrivals in an airport is exponentially distributed with a mean of 25 minutes.

(a) What is the probability of no arrivals for more than one hour?

(b) What is the probability of an arrival within 10 minutes?