Joint distributions of discrete random variables
... Often discrete RVs will not be independent. Their joint distribution can still be determined by use of the general multiplication rule. ...
... Often discrete RVs will not be independent. Their joint distribution can still be determined by use of the general multiplication rule. ...
1.3 Binomial Coefficients
... 1, because n0 is always 1, as it must be because there is just one subset of an n-element set with 0 elements, namely the empty set. Similarly, each row ends with a 1, because an n-element set S has just one n-element subset, namely S itself. Each row increases at first, and then decreases. Further t ...
... 1, because n0 is always 1, as it must be because there is just one subset of an n-element set with 0 elements, namely the empty set. Similarly, each row ends with a 1, because an n-element set S has just one n-element subset, namely S itself. Each row increases at first, and then decreases. Further t ...
Chapter 17: The binomial model of probability Part 3
... Binomial model: tying it all together What is a binomial?(2) • Either one variable and a constant or two variables, separated by an addition or subtraction sign so that there are, in fact, two terms • Each term of the binomial can have a numeric multiple, including fractions (i.e., division) and (w ...
... Binomial model: tying it all together What is a binomial?(2) • Either one variable and a constant or two variables, separated by an addition or subtraction sign so that there are, in fact, two terms • Each term of the binomial can have a numeric multiple, including fractions (i.e., division) and (w ...
The Poisson Distribution
... The plant manager of a toy manufacturing plant has been given an order for 10,000 new toys with a shipping date 10 weeks from now. He currently has 8 machines that produce 100 toys per week per machine, assuming one shift of 40 hours per week. He needs to know if the machines need to run overtime to ...
... The plant manager of a toy manufacturing plant has been given an order for 10,000 new toys with a shipping date 10 weeks from now. He currently has 8 machines that produce 100 toys per week per machine, assuming one shift of 40 hours per week. He needs to know if the machines need to run overtime to ...
Document
... How many ways are there to pick 2 successive cards from a standard deck of 52 such that: a. The first card is an Ace and the second is not a Queen? b. The first is a spade and the second is not a Queen? a) We are creating a list of two things. There are 4 choices for the first item and (51 – 4) = 47 ...
... How many ways are there to pick 2 successive cards from a standard deck of 52 such that: a. The first card is an Ace and the second is not a Queen? b. The first is a spade and the second is not a Queen? a) We are creating a list of two things. There are 4 choices for the first item and (51 – 4) = 47 ...
8.6 the binomial theorem
... for any positive integer power n, or to find any particular term in such an expansion. We begin by calculating the first few powers directly and then look for significant patterns. To go from one power of ~a 1 b! to the next, we simply multiply by ~a 1 b!: ~a 1 b!1 5 a 1 b ~a 1 b!2 5 a 2 1 2ab 1 b 2 ...
... for any positive integer power n, or to find any particular term in such an expansion. We begin by calculating the first few powers directly and then look for significant patterns. To go from one power of ~a 1 b! to the next, we simply multiply by ~a 1 b!: ~a 1 b!1 5 a 1 b ~a 1 b!2 5 a 2 1 2ab 1 b 2 ...
Algorithms for Distributions
... The Poisson Distribution The sampling methods given above can be used to generate observations from all of the common discrete distributions except for the Poisson which because of its infinite support and not being expressible in terms of simple sampling methods, requires special methods. Most meth ...
... The Poisson Distribution The sampling methods given above can be used to generate observations from all of the common discrete distributions except for the Poisson which because of its infinite support and not being expressible in terms of simple sampling methods, requires special methods. Most meth ...
B. The Binomial Theorem
... A general expression that we often encounter in algebra and calculus is (A + B)p . A and B denote real numbers; the exponent p might be an integer, although not necessarily. The binomial theorem tells how to expand this expression in powers of A and B. The simplest example is p = 2, which is familia ...
... A general expression that we often encounter in algebra and calculus is (A + B)p . A and B denote real numbers; the exponent p might be an integer, although not necessarily. The binomial theorem tells how to expand this expression in powers of A and B. The simplest example is p = 2, which is familia ...
Homework set 3
... the center of one wall. The rectangular wall has sides 6 by 8. Now the assumption is that all points on the wall are equally likely to be hit. In other words, the coordinates X and Y of a hit are uniformly distributed over the intervals [0, 6] and [0, 8], respectively. (a) What is the exact probabil ...
... the center of one wall. The rectangular wall has sides 6 by 8. Now the assumption is that all points on the wall are equally likely to be hit. In other words, the coordinates X and Y of a hit are uniformly distributed over the intervals [0, 6] and [0, 8], respectively. (a) What is the exact probabil ...
