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Susan assumes the stranger chose a fair coin (so the prior probability that the tossed coin is the unfair coin is 0). Consequently, Susan calculates the probability that three (or any number of consecutive heads) were tossed with the unfair coin must be 0; if still more heads are thrown, Susan does not change her probability.
In statistical decision theory, a randomised decision rule or mixed decision rule is a decision rule that associates probabilities with deterministic decision rules. In finite decision problems, randomised decision rules define a risk set which is the convex hull of the risk points of the nonrandomised decision rules.
In probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X. The form of the law depends on the type of random variable X in question.
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing one to find the probability of a cause given its effect. [1]
If X n converges in probability to X, and if P(| X n | ≤ b) = 1 for all n and some b, then X n converges in rth mean to X for all r ≥ 1. In other words, if X n converges in probability to X and all random variables X n are almost surely bounded above and below, then X n converges to X also in any rth mean. [10] Almost sure representation ...
Over and over at a confirmation hearing on Wednesday, Democratic senators confronted Robert F. Kennedy Jr. about controversial comments they said he had made in the past. And over and over ...
The FDA is seeking comments on the proposed rule from the public and industry representatives for the next 90 days before finalizing the requirements. (This story has been refiled to change the ...
Robert F. Kennedy Jr.'s confirmation hearing on Wednesday to lead the Department of Health and Human Services saw senators question the environmental lawyer about his views on vaccines, abortion ...