In the following probability distribution, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in.
x P(x) 0 0.272 10.575 20.121 30.027 40.004 50.001
(a) Verify that this is a discrete probability distribution.
(b) Draw a graph of the probability distribution. Describe the shape of the distribution.
(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 a randomly selected individual 15 years or older was involved in tow marriages?
(f) What is the probability that a randomly selected individual 15 years or older was involved in at least two marriges?
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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
|
x |
P(x) |
|
0 |
0.167 |
|
1 |
0.3289 |
|
2 |
0.2801 |
|
3 |
0.149 |
|
4 |
0.0382 |
|
5 |
0.0368
|
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?
a.Compute the theoretical mean of the random variable X for the given probability distribution.
Meu = ?
b. Compute the theoretical standard deviation of the random variable X for the given probability distribution.
Sigma =?
c.Approximate the mean of the random variable X based on the simulation for 25 games.
Xbar=?
d. Approximate the standard deviation of the random variable X based on the simulation for 25 games.
S=?
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 x P(x) 0 0.167 1 0.3289 2 0.2801 3 0.149 4 0.0382 5 0.0368 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? a.Compute the theoretical mean of the random variable X for the given probability distribution. Meu = ? b. Compute the theoretical standard deviation of the random variable X for the given probability distribution. Sigma =? c.Approximate the mean of the random variable X based on the simulation for 25 games. Xbar=? d. Approximate the standard deviation of the random variable X based on the simulation for 25 games. S=?
