Description
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 |
---|---|
4 | 19 |
5 | 27 |
6 | 24 |
7 | 36 |
8 | 1 |
Use the above table to answer the following questions:
- Explain what type of random variable W is.
- Find its sample space and probability distribution.
- Find its mean value and describe it in terms of the problem.
Explanation & Answer
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
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