compute the variable of the random varible X

Incomplete data.

If the standard deviation is $10, 000, can the president conclude that there is a difference?

At alpha = 0.10, is he correct?

To compute the variable of a random variable X, you need to be clear about what you mean by "variable."

If you are referring to the possible values that the random variable X can take, you need to look at the probability distribution of X. The probability distribution specifies the likelihood of each possible value occurring.

Here are the general steps to compute the possible values of X:

1. Identify the random variable X: Determine what X represents in the context of your problem. It could be the outcome of a dice roll, the number of cars passing through an intersection in one hour, or any other measurable quantity.

2. Determine the probability distribution: If you have information about the probability distribution of X, you can use it to find the possible values. The probability distribution can be described using different methods, such as a probability mass function (PMF) for discrete random variables or a probability density function (PDF) for continuous random variables.

3. Analyze the probability distribution: Depending on the type of random variable X, you can identify its possible values using various approaches. For discrete random variables, the possible values are usually listed explicitly in the PMF. For continuous random variables, the possible values are within a specific range determined by the PDF.

4. Compute the variable of X: Once you have the probability distribution and the possible values of X, you can analyze or compute various statistical measures related to X, such as the mean, variance, or standard deviation.

Note: It's important to have the probability distribution of X to accurately compute its variable. Without the probability distribution, it might not be possible to determine the possible values of X.