MATH 105 101
Assignment 5
Due date: November 13, 2014
MATH 105 101 Assignment 5
All work must be shown for full marks.
1. (7 marks) In a deck of 30 distinct cards, there is exactly one legendary card called
Deathwing. If Artosis draws a hand of 3 cards randomly from the deck (without
replacing the cards drawn):
• How many possible hands of 3 cards are there?
• What is the probability that he will draw the legendary card in his hand?
2. (9 marks) Let X be the duration of a telephone call in minutes and suppose that X
has the following probability density function:
f (x) = ce−x/10 for x ≥ 0, and c is some constant.
• Determine the value of c.
• What is the probability that a call lasts less than 5 minutes?
• Compute the expected value E(X).
3. (9 marks) Let X be a continuous random variable, with the following probability
density function:
(
a + bx2 , 0 ≤ x ≤ 1
f (x) =
0 else.
• Suppose that the expected value E(X) = 3/5, determine the values of a and b.
• Compute the variance Var(X).
Total: 25 marks.
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