The Metropolis-Hastings Algorithm and Extensions
... We assume here that X is endowed with an obvious, natural measure “dx”. If dx is counting measure on X (that is, each point in X has mass one), then E(F ) is a sum instead of an integral. We assume that we do not know the density π(x) exactly, but that we can calculate π(x) within the normalizing co ...
... We assume here that X is endowed with an obvious, natural measure “dx”. If dx is counting measure on X (that is, each point in X has mass one), then E(F ) is a sum instead of an integral. We assume that we do not know the density π(x) exactly, but that we can calculate π(x) within the normalizing co ...
Statistics for Business and Economics
... While measures of central tendency are useful to understand what are the typical values of the data, measures of dispersion are important to describe the scatter of the data or, equivalently, data variability with respect to the central tendency. Two distinct samples may have the same mean or median ...
... While measures of central tendency are useful to understand what are the typical values of the data, measures of dispersion are important to describe the scatter of the data or, equivalently, data variability with respect to the central tendency. Two distinct samples may have the same mean or median ...
Mapping for Instruction - First Nine Weeks
... Investigate and describe sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling. ...
... Investigate and describe sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling. ...
Poisson Random Variables
... Given P{X = k} = λk! e −λ for integer k ≥ 0, what is Var[X ]? Think of X as (roughly) a Bernoulli (n, p) random variable with n very large and p = λ/n. This suggests Var[X ] ≈ npq ≈ λ (since np ≈ λ and q = 1 − p ≈ 1). Can we show directly that Var[X ] = λ? ...
... Given P{X = k} = λk! e −λ for integer k ≥ 0, what is Var[X ]? Think of X as (roughly) a Bernoulli (n, p) random variable with n very large and p = λ/n. This suggests Var[X ] ≈ npq ≈ λ (since np ≈ λ and q = 1 − p ≈ 1). Can we show directly that Var[X ] = λ? ...
Relationships among some univariate distributions
... Figure 1 illustrates 35 univariate distributions in 35 rectangle-like entries. The row and column numbers are labeled on the left and top of Fig. 1, respectively. There are 10 discrete distributions, shown in the first two rows, and 25 continuous distributions. Five commonly used sampling distributio ...
... Figure 1 illustrates 35 univariate distributions in 35 rectangle-like entries. The row and column numbers are labeled on the left and top of Fig. 1, respectively. There are 10 discrete distributions, shown in the first two rows, and 25 continuous distributions. Five commonly used sampling distributio ...
STAT 107 – CONCEPTS OF STATISTICS Adopted Summer 2014
... understand the basic concept of probability and use it as a language to describe chance, variation, and risk understand the process of statistical inference and be able to draw conclusions about a population based on sample data read analytically results of statistical studies such as surveys and ex ...
... understand the basic concept of probability and use it as a language to describe chance, variation, and risk understand the process of statistical inference and be able to draw conclusions about a population based on sample data read analytically results of statistical studies such as surveys and ex ...
Reasoning Under Uncertainty
... • Agents have preferences over states of the world that are possible outcomes of their actions. • Every state of the world has a degree of usefulness, or utility, to an agent. Agents prefer states with higher utility. • Decision theory=Probability theory + Utility theory • An agent is rational if an ...
... • Agents have preferences over states of the world that are possible outcomes of their actions. • Every state of the world has a degree of usefulness, or utility, to an agent. Agents prefer states with higher utility. • Decision theory=Probability theory + Utility theory • An agent is rational if an ...
day10
... 6) Harman / Negreanu, and running it twice. Harman has 10 7 . Negreanu has K Q . The flop is 10u 7 Ku . Harman’s all-in. $156,100 pot. P(Negreanu wins) = 28.69%. P(Harman wins) = 71.31%. Let X = amount Harman has after the hand. If they run it once, E(X) = $0 x 29% + $156,100 x 71.31% = $111,3 ...
... 6) Harman / Negreanu, and running it twice. Harman has 10 7 . Negreanu has K Q . The flop is 10u 7 Ku . Harman’s all-in. $156,100 pot. P(Negreanu wins) = 28.69%. P(Harman wins) = 71.31%. Let X = amount Harman has after the hand. If they run it once, E(X) = $0 x 29% + $156,100 x 71.31% = $111,3 ...
Informal Outline of Risk Neutral Pricing In Continuous Time Jim Bridgeman
... all s, then V (t; S (t)) is a Replicating Portfolio, demonstrating that the Claim is Replicable. Conversely, every Replicating Portfolio for a Replicable Claim provides a solution to the equation for which V (T; S (T )) = P ayOf fT (S (T )). For a Replicable Claim in an Arbitrage-Free market model t ...
... all s, then V (t; S (t)) is a Replicating Portfolio, demonstrating that the Claim is Replicable. Conversely, every Replicating Portfolio for a Replicable Claim provides a solution to the equation for which V (T; S (T )) = P ayOf fT (S (T )). For a Replicable Claim in an Arbitrage-Free market model t ...