Economics FAQs: "Economics Essentials: Frequently Asked Questions Solved!"

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You use the given probability density function (PDF) for the time the book is checked out to compute the probability. For instance, suppose that the book checkout time ????X was described by the PDF ????????)f(x)=0.5x for 0≤x≤2. You then proceed to compute the probability for a range of times by integrating the PDF over the desired interval.

To find this probability, you would make use of a transition matrix that described the Markov process of bond ratings. This involved multiplying the transition matrix times itself for each period (in this case, two years) to determine the probability of the bond going from an AAA rating to Default.

"99% confidence" means that in repeated sampling, 99% of the intervals constructed from the data will contain the true population parameter (e.g., mean or proportion). This usually comes with confidence intervals with hypothesis testing.

In MATLAB, you can generate random variables using functions like randn and rand, and then use the formula for the correlation coefficient to assess the relationships between variables. You would calculate the covariance between two variables and then divide by the product of their standard deviations.

A process is wide-sense stationary if its mean is constant with time, its autocovariance function depends only on the time difference (lag), and its variance is finite and constant with time.

The autocorrelation function of a random process is the correlation of the process with a lagged version of itself. It can be calculated using the expected value of the product of the process at two different time points, with the lag as a parameter.

If diameters of bearing shafts are normally distributed with known mean and standard deviation, then one may apply the normal distribution to determine the probability of a shaft being rejected (i.e., falling outside the specified range).

It computes the relationship between two variables with respect to randomness. That means when the covariance is positive it is said that variables together increased otherwise the variables are in decreasing relationship if it's negative. Covariance measures importance about the linear relationship and for studying if any of the random variables depend or independent.

In essence, two random variables are independent if the covariance between them is zero. A zero covariance, however does not guarantee that there will be no relationship among variables, particularly if that relationship is not linear in nature.

If the failure of each device in a circuit is independent, then you can use the binomial distribution or a similar probability model to calculate the probability of having a specific number of failures, like two or fewer failures, for a particular configuration.