Contents
What is positive dependence?
Positive dependence in this case means that the set of tests are positively correlated. The idea then is that if the variables in the set of tests that you have P-values for are positively correlated then each of the variables are not independent.
What are expection of a function of random variables?
The expectation of Bernoulli random variable implies that since an indicator function of a random variable is a Bernoulli random variable, its expectation equals the probability. Formally, given a set A, an indicator function of a random variable X is defined as, 1A(X) = { 1 if X ∈ A 0 otherwise .
What is negatively dependent?
A stronger property, called negative regression dependence (in analogy with positive regression dependence c.f. Esary, Proschan and Walkup 1967), is defined by requiring the conditional distribution of X given Y to be stochastically decreasing in Y : P(X ≥ t|Y = s) is decreasing in s for each t.
How are random variables x and Y independent?
Random variables X and Y are independent if their joint distribution function factors into the product of their marginal distribution functions • Theorem. Suppose X and Y are jointly continuous random variables. X and Y are independent if and only if given any two densities for X and Y their product is the joint density for the pair (X,Y) i.e.
Which is an independent function of a random vector?
Therefore, and are independent. Let be a continuous random vector with support and its joint probability density function be Are and independent?
What is the expectation of a Cauchy random variable?
A Cauchy random variable takes a value in (−∞,∞) with the fol- lowing symmetric and bell-shaped density function. f(x) = 1 π[1+(x−µ)2] The expectation of Bernoulli random variable implies that since an indicator function of a random variable is a Bernoulli random variable, its expectation equals the probability.
What do you call a random variable that takes on infinite values?
A random variable that takes on a finite or countably infinite number of values (see page 4) is called a dis- crete random variablewhile one which takes on a noncountably infinite number of values is called a nondiscrete random variable. Discrete Probability Distributions