The probability distribution of the random variable X represents the number of h
ID: 3228465 • Letter: T
Question
The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season.
The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?
Table of the numbers of hits for 25 games.
Table of the numbers of hits for 50 games.
x 0 1 2 3 4 5 P(x) 0.2061 0.3391 0.2996 0.0752 0.0753 0.0047Explanation / Answer
Solution
Table - 1 and Table - 2 below give the frequency distribution of 25 and 50 simulated figures respectively alongwith certain related figures [Note: pi represents the given probabilities and picap represents the simulated proportion]
Table - 1
x
0
1
2
3
4
5
Total
f(x)
6
9
7
1
2
0
25
picap
0.24
0.36
0.28
0.04
0.08
0
1.00
pi - picap
-.0.0339
- 0.0209
0.0196
-0.0352
- 0.0047
0.0047
0
Table - 2
x
0
1
2
3
4
5
Total
f(x)
10
17
15
4
4
0
50
picap
0.20
0.34
0.30
0.08
0.08
0
1.00
pi - picap
.0.0061
- 0.0009
- 0.0004
-0.0048
- 0.0047
0.0047
0
Conclusion
As number of simulation increases from 25 to 50, the difference (pi - picap) comes down drastically bringing out the base of simulation that as n increases, simulated values get closer and closer to the actual values.
DONE
x
0
1
2
3
4
5
Total
f(x)
6
9
7
1
2
0
25
picap
0.24
0.36
0.28
0.04
0.08
0
1.00
pi - picap
-.0.0339
- 0.0209
0.0196
-0.0352
- 0.0047
0.0047
0
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