TAILIEUCHUNG - Ebook A first course in probability (5th edition): Part 2

(BQ) Part 2 book "A first course in probability" has contents: Limit theorems, additional topics in probability, simulation, the simple Matlab calculations for this problem, Matlab calculations for this problem,. and other contents. | 394 Chapter 7 Properties of Expectation 11. The nine players on a basketball team consist of 2 centers 3 forwards and 4 backcourt players. If the players are paired up at random into three groups of size 3 each find the a expected value and the b variance of the number of triplets consisting of one of each type of player. 12. A deck of 52 cards is shuffled and a bridge hand of 13 cards is dealt out. Let X and Y denote respectively the number of aces and the number of spades in the dealt hand. a Show that X and Y are uncoưelated. b Are they independent 13. Each coin in a bin has a value attached to it. Each time that a coin with value p is flipped it lands on heads with probability p. When a coin is randomly chosen from the bin its value is uniformly distributed on 0 1 . Suppose that after the coin is chosen but before it is flipped you must predict whether it will land heads or tails. You will win 1 if you are coưect and will lose 1 otherwise. a What is your expected gain if you are not told the value of the coin b Suppose now that you are allowed to inspect the coin before it is flipped with the result of your inspection being that you learn the value of the coin. As a function of p the value of the coin what prediction should you make c Under the conditions of part b what is your expected gain 14. In Self-Test Problem 1 we showed how to use the value of a uniform 0 1 random variable commonly called a random number to obtain the value of a random variable whose mean is equal to the expected number of distinct names on a list. However its use required that one chooses a random position and then determine the number of times that the name in that position appears on the fist. Another approach which can be more efficient when there is a large amount of name replication is as follows. As before start by choosing the random variable X as in Problem 3. Now identify the name in position X and then go through the list starting at the beginning until that name appears. Let

• Toán học
• A first course in probability
• Limit theorems
• Additional topics in probability
• The simple Matlab
• Matlab calculations for this problem
• Axioms of probability
• Combinatorial analysis
• Conditional probability
• Random variables
• Continuous random variables
• Jointly distributed random variables
• Properties of expectation