Group 4 Discrete Probability

a method that was introduced by Paul Erd˝os and Alfr´ed R´enyi that can be used to create nonconstructive existence proofs

• Probabilistic Method

• Geometric Distribution

• Average-Case Computational Complexity

• Monte Carlo

It is an algorithm for a decision problem uses a sequence of tests. The probability that the algorithm answers the decision problem correctly increases as more tests are carried out.

• Bernoulli Trials

• Bayes Algorithms

• Monte Carlo Algorithms

• Chebyshev’s Inequality

A coin is biased so that the probability of heads is 2∕3. What is the probability that exactly four heads come up when the coin is flipped seven times, assuming that the flips are independent?

• 880/3245

• 550/2187

• 770/3245

• 560/2187

When a coin is flipped, the possible outcomes are heads and tails. Each performance of an experiment with two possible outcomes is called a ?

• Bayes Theorem

• Bernoulli Trials

• independent events

• Conditional Probability

Expected Value of a Die Let X be the number that comes up when a fair die is rolled. What is the expected value of X?

• 7/2

• 5/2

• 21/5

• 24/5

says that the expected value of a sum of random variables is equal to the sum of the individual expectations.

• Division of expectations

• The Geometric Distribution

• Average-Case Computational Complexity

• Linearity of Expectations

How likely is it that a random variable takes a value far from its expected value? What answers this question?

• Bayes Theorem

• Monte Carlo Theorem

• Chebyshev’s Inequality

• Independent Random Variables

What is the expected sum of the numbers that appear on two dice, each biased so that a 33 comes up twice as often as each other number?

• 6.86

• 6.87

• 6.85

• 6.84

A coin is biased so that the probability a head comes up when it is flipped is 0.6. What is the expected number of heads that come up when it is flipped 10 times?

• 5

• 6

• 7

• 4

The expected value of a random variable is the _____ over all elements in a sample space of the product of the probability of the element and the value of the random variable at this element.

• product

• average

• sum

• difference