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

Statistics
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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

Thank you for the opportunity to help you with your question!

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





Please let me know if you need any clarification. I'm always happy to answer your questions.
Jan 14th, 2016

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