User talk:Gknauth

Welcome!

Hello,, and welcome to Wikipedia! I hope you like the place and decide to stay. Unfortunately, one or more of the pages you created may not conform to some of Wikipedia's guidelines for page creation, and may soon be deleted.

There's a page about creating articles you may want to read called Your first article. If you are stuck, and looking for help, please come to the New contributors' help page, where experienced Wikipedians can answer any queries you have! Or, you can just type   on this page, and someone will show up shortly to answer your questions. Here are a few other good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes ( ~ ); this will automatically produce your name and the date. If you have any questions, check out Where to ask a question or ask me on. Again, welcome! Qwfp (talk) 19:44, 4 April 2009 (UTC)
 * Your first article
 * Biographies of living persons
 * How to write a great article
 * The five pillars of Wikipedia
 * Help pages
 * Tutorial

Proposed deletion of Loyer's paradox
A proposed deletion template has been added to the article Loyer's paradox, suggesting that it be deleted according to the proposed deletion process&#32; because of the following concern:
 * Non-Notable neologism with 0 google hits

All contributions are appreciated, but this article may not satisfy Wikipedia's criteria for inclusion, and the deletion notice should explain why (see also "What Wikipedia is not" and Wikipedia's deletion policy). You may prevent the proposed deletion by removing the  notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page.

Please consider improving the article to address the issues raised because, even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached. Qwfp (talk) 19:44, 4 April 2009 (UTC)

begin excerpt from article


The data produce a paradox wherein the unconditional probability of the pinch-hitter getting a hit is greater than any of the conditional probabilities. In formal notation,


 * The unconditioned probability of a hit is
 * $$P(H) = {\frac 1 2}(.260) + {\frac 1 2}(.360) = .310$$


 * The conditional probability of a hit given the pitcher is left-handed is
 * $$P(H \mid L) = {\frac 1 2}(.300) + {\frac 1 2}(.240) = .270$$


 * The conditional probability of a hit given the pitcher is right-handed is
 * $$P(H \mid R) = {\frac 1 2}(.100) + {\frac 1 2}(.480) = .290$$

end excerpt from article
After the words "In formal notation", the coefficients of 1/2 in the first line of TeX mean that the probability that Arnie is chosen is 1/2 and the probability that Barnie is chosen is 1/2. In the second and third lines of TeX, the coefficients equal to 1/2 mean that the conditional probability that Arnie is chosen, given that the pitcher is left-handed, is 1/2, and the same for Barney, and the conditional probability that Arnie is chosen, given that the pitcher is right-handed, is 1/2, and the same for Barney. That implies that the choice of Arnie or Barney is independent of the handedness of the pitcher. '''This independence means the probability of getting a left-handed pitcher is the same for the two batters. But the table above treats them as different. That is the essential error.' Once we know they're independent, then to complete the probability model, we need only know the probability p of getting a left-handed pitcher (and then 1 &minus; p'' is the probability of a right-handed pitcher). Then we can say Arnie's "overall average", i.e. his probability of getting a hit, is

\begin{align} \Pr(\text{hit} \mid \text{Arnie}) & = \Pr(\text{hit} \mid \text{LH and Arnie})\Pr(\text{LH}) + \Pr(\text{hit} \mid \text{RH and Arnie})\Pr(\text{RH}) \\ & = 0.3 p + 0.1(1-p) \\ & = 0.2p + 0.1. \end{align} $$ Similarly Barney's overall probability of a hit is

\begin{align} \Pr(\text{hit} \mid \text{Barney}) & = \Pr(\text{hit} \mid \text{LH and Barney})\Pr(\text{LH}) + \Pr(\text{hit} \mid \text{RH and Barney})\Pr(\text{RH}) \\ & = 0.24 p + 0.48(1-p) \\ & = 0.48 - 0.24p. \end{align} $$ Then the unconditioned probability of a hit is

\begin{align} \Pr(\text{hit}) & = \Pr(\text{hit} \mid \text{Arnie})\Pr(\text{Arnie}) + \Pr(\text{hit} \mid \text{Barney})\Pr(\text{Barney}) \\ & = \frac 1 2 (0.2p + 0.1) + \frac 1 2 (0.48 - 0.24p) \\ & = 0.29 - 0.02p. \end{align} $$ The conditional probability of a hit given a left-handed pitcher is

\begin{align} \Pr(\text{hit} \mid \text{LH}) & = \Pr(\text{Arnie})\Pr(\text{hit} \mid \text{LH and Arnie}) + \Pr(\text{Barney})\Pr(\text{hit} \mid \text{LH and Barney}) \\ & = \frac 1 2 (0.3) + \frac 1 2 (0.24) \\ & = 0.27. \end{align} $$ Similarly, the conditional probability of a hit given a right-handed pitcher is

\begin{align} \Pr(\text{hit} \mid \text{RH}) & = \Pr(\text{Arnie})\Pr(\text{hit} \mid \text{RH and Arnie}) + \Pr(\text{Barney})\Pr(\text{hit} \mid \text{RH and Barney}) \\ & = \frac 1 2 (0.1) + \frac 1 2 (0.48) \\ & = 0.29. \end{align} $$ The question now is: Is the unconditional probability of a hit BETWEEN the conditional probability of a hit given LH, and the conditional probability of a hit given RH?

I.e. is 0.29 &minus; 0.02p between 0.27 and 0.29?

The answer is "yes", since p is between 0 and 1. If p = 0, then the probability is 0.29. If p = 1, then the probability is 0.27.

So the claim in the article is false.

The error entered at the point where the article's author based the "overall average" on the historical frequency with which Arnie faced left- and right-handed batters. It should have been based instead on the probabilities of his facing left- and right-handed batters in the proposed scenario.

Notice that
 * $$ \Pr(\text{hit}) = \Pr(\text{hit} \mid \text{LH})\Pr(\text{LH}) + \Pr(\text{hit} \mid \text{RH})\Pr(\text{RH}), \, $$

and that is enough to prove that the unconditional probability of a hit must lie between the two conditional probabilities. In this connection, see also law of total probability. Michael Hardy (talk) 03:30, 7 April 2009 (UTC)

Nomination for deletion
I've nominated the article titled Loyer's paradox for deletion. The discussion is here. If you can replace the article with content worth keeping under the same article title, I'll withdraw the nomination. Michael Hardy (talk) 23:54, 7 May 2009 (UTC)