exercise:Efb67bfff5: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> A baseball player is to play in the World Series. Based upon his season play, you estimate that if he comes to bat four times in a game the number of hits he will get has a distribution <math display="block"> p_X = \pmatrix{ 0 & 1 & 2 & 3 & 4 \c...") |
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A baseball player is to play in the World Series. Based upon his season play, you estimate that if he comes to bat four times in a game the number of | |||
play, you estimate that if he comes to bat four times in a game the number of | |||
hits he will get has a distribution | hits he will get has a distribution | ||
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Assume that the player comes to bat four times in each game of the series. | Assume that the player comes to bat four times in each game of the series. | ||
<ul><li> | <ul style="list-style-type:lower-alpha"><li> | ||
Let <math>X</math> denote the number of hits that he gets in a series. Using the program ''' | Let <math>X</math> denote the number of hits that he gets in a series. Using the program '''NFoldConvolution''', find the distribution of <math>X</math> for each of the possible series lengths: | ||
NFoldConvolution''', find the distribution of <math>X</math> for each of the possible series lengths: | |||
four-game, five-game, six-game, seven-game. | four-game, five-game, six-game, seven-game. | ||
</li> | </li> | ||
Latest revision as of 23:59, 24 June 2024
A baseball player is to play in the World Series. Based upon his season play, you estimate that if he comes to bat four times in a game the number of hits he will get has a distribution
[[math]]
p_X = \pmatrix{
0 & 1 & 2 & 3 & 4 \cr
.4 & .2 & .2 & .1 & .1\cr}.
[[/math]]
Assume that the player comes to bat four times in each game of the series.
- Let [math]X[/math] denote the number of hits that he gets in a series. Using the program NFoldConvolution, find the distribution of [math]X[/math] for each of the possible series lengths: four-game, five-game, six-game, seven-game.
- Using one of the distribution found in part (a), find the probability that his batting average exceeds .400 in a four-game series. (The batting average is the number of hits divided by the number of times at bat.)
- Given the distribution [math]p_X[/math], what is his long-term batting average?