Maybe the 162 is related to number of games in a major league regular season.
Gerry On Thu, 13 Mar 2003 14:15:03 -0500, Paige Miller <[EMAIL PROTECTED]> wrote: >Fred Ettish wrote: > > I was given this problem and and having some difficulty understanding > > part of it. > > > > The problem involves a .250 hitter who gets 5 at bats per game and > > the question is ( I think) "What is the expected streak of games > > where the batter gets a hit?" > > > > So > > > > The probability of not getting a hit at bat is .750. The probability > > of no hits at 4 at bats is .750^5 = .237 The probability of at least > > one hit per game is 1 - .237 = .763 > >You are in good shape up to here, if my assumption of typographical >error is correct (specifically, the above should read "probability >of no hits at 5 at bats") > >At this point, to get the expected consecutive number of games in which >a batter gets a hit, you would have a geometric distribution with >probability p=0.763 for each trial. Thus, expected value is 1/p = >1/0.763 = well you can figure it out from here > > > So the longest streak is k where .763^k=1/162 > > > > Can anyone explain this last step? Why set it equal to 1/162? > >I can't explain it. > > > Thanks > >Now, all of this also makes the assumption that the probability of >getting a hit each and every at bat is the same, a dubious assumption, >but perhaps a place to start. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
