(a) Finding Expected Value, Variance, and Standard Deviation In use the given probability density function over the indicated interval to find the (a) expected value,
(b) Variance using the alternative formula, and
(c) Standard deviation of the random variable.
(a) Finding Expected Value, Variance, and Standard Deviation In use the given probability density function over the indicated interval to find the (a) expected value,
(b) Variance using the alternative formula, and
(c) Standard deviation of the random variable.
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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=?
