Question

If \({\bf{X}}\)has the \({\bf{p}}.{\bf{d}}.{\bf{f}}.\)\({\bf{1/}}{{\bf{x}}^{\bf{2}}}\)for\({\bf{x > 1}}\), the mean of \({\bf{X}}\) is infinite. What would you expect to happen if you simulated a large number of random variables with this \({\bf{p}}.{\bf{d}}.{\bf{f}}.\) and computed their average?

Short answer

The mean would increase as number of observations increases.

Step-by-step solution

Definition for simulation

• Simulation is model-based experimentation.
• The model's behaviour imitates some salient aspect of the system under study's behaviour, and the user experiments with the model to infer this behaviour.
• This broad framework has proven to be an effective tool for learning, problem solving, and design.
• A probability density function (PDF) is a statistical expression that defines a probability distribution (the likelihood of an outcome) for a discrete random variable (for example, a stock or ETF) rather than a continuous random variable.

Determine the computation of average

• Random variable\(X\)takes values which for large\(x\)get smaller.
• By simulating large number,\(n\)of such variables, the average would get bigger as\(n\)increases.
• This is because some values would be much larger then the others, which would appear more frequently when the number of observations increases. When the large observations appear, the mean increases.