1. Give a recursive definition for the sequence: 2, 4, 8, 16, 32 ? 2. Let f(x)...
Question:
1. Give a recursive definition for the sequence: 2, 4, 8, 16, 32 ?
2. Let f(x) = -2f(x-1) + 5 and f(0) = 2, find f(4).
3. In New York City, there are two non-bald people who have the same number of hairs on their head. (The human head can contain up to several hundred thousand hairs, with a maximum of about 500,000.)
4. Imagine BMCC has 25,000 students, at least one from each of the 50 states. Then there must be a group of 500 students coming from same state.
5 & 6 : For each situation, decide if the random variable described is a discrete random variable or a continuous random variable.
5. Random variable X = the number of letters in the last name of a student picked at random from a class on English composition.
- Discrete random variable
- Continuous random variable
6. Random variable X = the time (seconds) it takes one email to travel between a sender and receiver.
- Discrete random variable
- Continuous random variable
7 to 9 : The probability distribution for X = number of heads in 4 tosses of a fair coin is given in the table below.
7. What is the probability of getting at least one head?
- 1/16
- 4/16
- 5/16
- 15/16
8. What is the probability of getting 1 or 2 heads?
- 4/16
- 6/16
- 10/16 D.14/16
9. What is the value of the cumulative distribution function at 3, i.e. P(X ? 3)?
- 6/16
- 10/16
- 11/16 D.15/16
10. For the relation on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is anti-symmetric, and whether it is transitive. In order to get full credits: For example, if it?s not reflexive, you must state why it is not. {(1, 1), (1, 2), (2, 3), (2, 4), (3, 2), (3, 3)}
Reflexive:
Symmetric:
Anti-symmetric:
Transitive: