## Example 51 Calculating Skew For Three Small Samples

As an illustration, consider three separate samples of a random variable as shown in Table 5.1. Each sample has a mean of approximately 0 and a standard deviation of approximately 1. However, in this case the mean and standard deviation do not provide enough information to adequately summarize the data. On close inspection you will observe that sample 1 is symmetric around 0, sample 2 negatively skewed, and sample 3 positively skewed. Using the above formula, we estimate the skew for sample 1...

## Excel and VBA Functions for Correlation Covariance and Variance

The correlation between two variables can be calculated in Excel using the Correl() function. Covariance can be calculated using the Covar() function. Given a sample of risk indicators or OR events, the variance and standard deviation are best calculated using the Var() and Stdev() functions, respectively. An alternative, if we have the entire population, is to use the TABLE 3.4 Subjective Probabilities of System Downtime Provided by Total cost 12,GGG + ( 1,125 x X ) Expected cost 12,GGG + (...

## The Law Of Significant Digits

Benford's law of significant digits states that a sample of the first significant and subsequent digits of numbers drawn from a wide variety of random probability distributions will have a certain form as the sample size becomes increasingly large. The law is actually based on a conjecture by the astronomer and mathematician Simon Newcomb. In a two-page article in 1881 in the American Journal of Mathematics, Newcomb conjectured that the probability that a number has first significant digit d is...

## General Beta Distribution

In this section we have described the standard beta distribution. There is a more general beta distribution that can be used when the random variable x lies in the interval a, b . The cumulative density function can be calculated in Excel using the function BETADIST x,alpha, beta,a,b . The simulation in the worksheet Beta Estimation in the workbook Operational Risk 07.xls used the inverse beta function BETAINV x,alpha,beta,a,b with parameters BETAINV RAND ,alpha, beta,0,1 . become closer to the...

## Useful Excel Functions

Excel has many probability and related functions of value in OR management. One of the most useful is the Percentile function, which returns the percentile of a given data set. It is illustrated in the workbook Operational Risk 02.xls worksheet Case study 2.2 and also discussed further in review question 6 below. Other valuable functions include the Normsinv , which calculates the percentile function for a standard normally distributed random variable, and Normsdist , which calculates the...

## Review Questions

List four examples of random experiments alongside their associated random variables. From your list identify the continuous and discrete random variables. 2. Identify four potential OR events. What do you think are potential risk indicators for these OR events and why 3. Can you explain why probability is useful for describing OR events 4. Suppose the probability of the event a serious transaction error is 0.2 and the probability of the event computer system failure and a serious...

## With Excel and VBA

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