For what p is Var X maximum

Thread starter TomJerry
Start date Nov 28, 2010
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In summary, "Var X" in this context refers to the variance of a random variable X, which measures the spread or variability of the data points around the mean. The maximum value of Var X is determined by finding the value of p that maximizes the variance, typically by taking the derivative of the variance function and setting it equal to 0. This allows us to understand the range of possible values for X and their likelihood, making it useful in statistical analysis and decision making. The maximum value of Var X cannot be negative, as the variance is always a non-negative value. Real-world applications for determining the maximum value of Var X include finance, manufacturing, and medicine.

Nov 28, 2010

TomJerry

Let the random variable X have the distribution

[itex]P(X=0) = P(=2) = p[/itex]

[itex]P(X=1) = 1-2p, [/itex] [itex]0 \le p \le \frac{1}{2}[/itex]

For what p is Var X maximum

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Nov 28, 2010

statdad

Homework Helper

Write down the expression for the variance - it will be a function of p. Maximize that function.

1. What is the definition of "Var X" in this context?

In this context, "Var X" refers to the variance of a random variable X, which measures the spread or variability of the data points around the mean.

2. How is the maximum value of Var X determined?

The maximum value of Var X is determined by finding the value of p that maximizes the variance. This is typically done by taking the derivative of the variance function with respect to p and setting it equal to 0, then solving for p.

3. What is the significance of determining the maximum value of Var X?

Determining the maximum value of Var X allows us to understand the range of possible values for the random variable X and how likely each of these values is to occur. This information is important in statistical analysis and decision making.

4. Can the maximum value of Var X be negative?

No, the maximum value of Var X cannot be negative. The variance is always a non-negative value, meaning that the data points cannot be more spread out than the maximum variance value.

5. Are there any real-world applications for determining the maximum value of Var X?

Yes, there are many real-world applications for determining the maximum value of Var X. For example, in finance, the maximum variance of a stock's returns can help investors understand the risk associated with that stock. In manufacturing, the maximum variance of a product's dimensions can help ensure consistency in production. In medicine, the maximum variance of a treatment's effectiveness can guide doctors in making treatment decisions.