Simulation Use the probability distribution from a
Chapter 6, Problem 35E(choose chapter or problem)
Problem 35E
Simulation Use the probability distribution from Problem and a DISCRETE command for some statistical software to simulate 100 repetitions of the experiment (100 games). The number of hits is recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. Repeat the simulation by performing 500 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?
Problem
Ichiro’s Hit Parade In the 2004 baseball season, Ichiro Suzuki of the Seattle Mariners set the record for the most hits in a season with a total of 262 hits. In the following probability distribution, the random variable X represents the number of hits Ichiro obtained in a game.
x |
P(x) |
0 |
0.1677 |
1 |
0.3354 |
2 |
0.2857 |
3 |
0.1491 |
4 |
0.0373 |
5 |
0.0248 |
(a) Verify that this is a discrete probability distribution.
(b) Draw a probability histogram.
(c) Compute and interpret the mean of the random variable X.
(d) Compute the standard deviation of the random variable X.
(e) What is the probability that in a randomly selected game Ichiro got 2 hits?
(f) What is the probability that in a randomly selected game Ichiro got more than 1 hit?
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