Goals of this section Define: • random variables. • discrete random
... Var(aX + b) = a2Var(X) and the SD of aX + b is |a| times the SD of X. ...
... Var(aX + b) = a2Var(X) and the SD of aX + b is |a| times the SD of X. ...
(1997). Sharpness of second moment criteria for branching and tree
... Trees with the same polar sets are denoted equipolar by Pemantle and Peres (1994). In particular, letting {X(v)} be uniform on the unit interval and letting B = {(x1 , x2 , . . .) : ∀n xn ≤ pn }, one sees that equipolar trees Γ1 and Γ2 are percolation equivalent, meaning that: If vertices of both tr ...
... Trees with the same polar sets are denoted equipolar by Pemantle and Peres (1994). In particular, letting {X(v)} be uniform on the unit interval and letting B = {(x1 , x2 , . . .) : ∀n xn ≤ pn }, one sees that equipolar trees Γ1 and Γ2 are percolation equivalent, meaning that: If vertices of both tr ...
Solution - Statistics
... 4. Consider the following approach to shuffling a deck of n cards. Starting with any initial ordering of the cards, one of the numbers 1, 2, . . . , 52 is chosen at random and with equal probability. If number i is chosen, we move the card from position i in the deck to the top, i.e. to position 1. ...
... 4. Consider the following approach to shuffling a deck of n cards. Starting with any initial ordering of the cards, one of the numbers 1, 2, . . . , 52 is chosen at random and with equal probability. If number i is chosen, we move the card from position i in the deck to the top, i.e. to position 1. ...
2017 Year12 Mathematics Methods ATAR Program
... develop the concepts of a discrete random variable and its associated probability function, and their use in modelling data use relative frequencies obtained from data to obtain point estimates of probabilities associated with a discrete random variable identify uniform discrete random variables and ...
... develop the concepts of a discrete random variable and its associated probability function, and their use in modelling data use relative frequencies obtained from data to obtain point estimates of probabilities associated with a discrete random variable identify uniform discrete random variables and ...
On the asymptotic equidistribution of sums of independent
... where (xe(0, 1] and Q and R are probability meassuch that Q is strongly nonlattice and concentrated on a bounded interval. If PTitself is concentrated on a bounded interval, this is trivial. ...
... where (xe(0, 1] and Q and R are probability meassuch that Q is strongly nonlattice and concentrated on a bounded interval. If PTitself is concentrated on a bounded interval, this is trivial. ...
random numbers
... but obviously are reproducible on the computers and therefore are not truly random. A useful definition of true random numbers is lack of correlations. If we consider the product of two random numbers r1 and r2 , -- r1 ⋅ r2 and we average over possible values of r1 and r2 , we should have r1 ⋅ r2 = ...
... but obviously are reproducible on the computers and therefore are not truly random. A useful definition of true random numbers is lack of correlations. If we consider the product of two random numbers r1 and r2 , -- r1 ⋅ r2 and we average over possible values of r1 and r2 , we should have r1 ⋅ r2 = ...
Serie Research Memoranda Spectra! characterization of the optional quadratic variation process
... time, the periodogram can be used for estimation problems in the frequency domain. It follows from the results of the present paper that the periodogram can also be used to estimate the variance of the innovations of a time series in continuous time. Usually in statistical problems this variance is ...
... time, the periodogram can be used for estimation problems in the frequency domain. It follows from the results of the present paper that the periodogram can also be used to estimate the variance of the innovations of a time series in continuous time. Usually in statistical problems this variance is ...
Lagrange Error Bound Notes
... Historically the remainder was not due to Taylor but to a French mathematician, Joseph Louis Lagrange (1736 – 1813). For this reason, Rn x is called the Lagrange form of the remainder or the Lagrange Error Bound. When applying Taylor’s Formula, we may or may not be able to find the exact value o ...
... Historically the remainder was not due to Taylor but to a French mathematician, Joseph Louis Lagrange (1736 – 1813). For this reason, Rn x is called the Lagrange form of the remainder or the Lagrange Error Bound. When applying Taylor’s Formula, we may or may not be able to find the exact value o ...
Stochastic Process
... o Ergodic theorems: sufficient condition for ergodic property. A process possesses ergodic property if the time/empirical averages converge (to a r.v. or deterministic value) in some sense (almost sure, in probability, and in p-th mean sense). Laws of large numbers Mean Ergodic Theorems in L^p s ...
... o Ergodic theorems: sufficient condition for ergodic property. A process possesses ergodic property if the time/empirical averages converge (to a r.v. or deterministic value) in some sense (almost sure, in probability, and in p-th mean sense). Laws of large numbers Mean Ergodic Theorems in L^p s ...
23A Discrete Random Variables
... P ( a < Y £ b) A _________________ random variable X has a finite or countable number of possible values. For example: M = the number of mobile telephones that you own, B = the number of bicycles that each family has. In general to determine the value of a discrete random variable we need to _______ ...
... P ( a < Y £ b) A _________________ random variable X has a finite or countable number of possible values. For example: M = the number of mobile telephones that you own, B = the number of bicycles that each family has. In general to determine the value of a discrete random variable we need to _______ ...
TEICHIB`S STRONG LAW OF LARGE NUMBERS IN GENERAL
... [I], CBoi- and Sung [Z] and Kuelbs and Zinn [ 5 ] have shown that many classical strong laws of large numbers (SLLN) hold for random variables taking values in a general Banach space under the assumption that the weak law of Iarge numbers (WLLN) holds; this assumption often follows from the geometri ...
... [I], CBoi- and Sung [Z] and Kuelbs and Zinn [ 5 ] have shown that many classical strong laws of large numbers (SLLN) hold for random variables taking values in a general Banach space under the assumption that the weak law of Iarge numbers (WLLN) holds; this assumption often follows from the geometri ...
Binomial Theorem
... different notations to mean the same thing. The parenthetical bit above has these equivalents: ...
... different notations to mean the same thing. The parenthetical bit above has these equivalents: ...
joaquin_dana_ca08
... The central limit theorem basically says that the more random variables are summed up together, their sum’s distribution will appear more Gaussian, no matter what the original probability distribution looked like. Therefore, if 100 random variables all had an exponential PDF, when added all together ...
... The central limit theorem basically says that the more random variables are summed up together, their sum’s distribution will appear more Gaussian, no matter what the original probability distribution looked like. Therefore, if 100 random variables all had an exponential PDF, when added all together ...
Lecture 2: Probability and Statistics (continued)
... R lies between -1 and 1; R = 1 if Y = X (perfect correlation), R = −1 if Y = −X (perfect anticorrelation), and R = 0 if X and Y are independent. Unlike covariance, R is not additive. The correlation coefficient is useful for describing how strongly X and Y are linearly related, but will not perfectl ...
... R lies between -1 and 1; R = 1 if Y = X (perfect correlation), R = −1 if Y = −X (perfect anticorrelation), and R = 0 if X and Y are independent. Unlike covariance, R is not additive. The correlation coefficient is useful for describing how strongly X and Y are linearly related, but will not perfectl ...
