Statistics World Series question Explain what type of random variable W is, statistics homework help

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A sports writer wants to learn about the distribution of games per Wold Series. Let W be the number of games that are played per best of seven World Series. Results from the last 107 World Series, which can be assumed to be enough, follow:

No. of games played in a best of seven World Series (w)World Series
19
27
24
36

Use the above table to answer the following questions:

1. Explain what type of random variable W is.
2. Find its sample space and probability distribution.
3. Find its mean value and describe it in terms of the problem.
Jan 14th, 2016

1. W is a discrete random variable because it is countable number of distinct values.

2. Sample space represents the sum of all possible outcomes. In this question our sample space = {4, 5, 6, 7, 8}, i.e., in case World Series takes place either 4,5,6,7 or 8 games will be played.

 Probability distribution
 w 4 5 6 7 8 P(w) 0.18 0.25 0.22 0.34 0.01

Workings

19/107=0.18, 27/107=0.25, 24/107=0.22, 36/107= 0.34 and 1/107=0.01

3. Mean value

E(W)= Σ{wi.P(wi)}

= (4*0.18)+(5*0.25)+(6*0.22)+(7*0.34)+(8*0.01)=5.75

On average, 6 games are played per every world series.

NB: The star sign represents multiplication

Jan 14th, 2016

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Jan 14th, 2016
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Jan 14th, 2016
Jun 25th, 2017
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