Below is a typical cumulative Z-value lookup. The Z value of 1.350 means “The value of 5.0 is 1.350 standard deviations above the mean of 2.30.” Now we can use the common Z table to retrieve the associated probability. A standard normal variable has zero mean and variance of one (consequently its standard deviation is also one). The first step is to standardize the given value of 5.0 into a Z value (aka, Z score):Īll we’ve done here is translate a normal variable into a standard normal variable. Parsimony here refers to the normal conveniently has only two parameters, mean and variance. ![]() The normal distribution is rarely realistic, but it is popular for learning purposes due to its special properties and what is called parsimony. I hope you noticed the phrase “normally distributed?” It comes up often in exams. Here is same question re-phrased: If an asset’s daily return is normally distributed with mean of 2.30% and daily volatility of 2.00%, what is the probability the asset’s return will be at least 5.0%? The same question could be re-phrased into the language of asset returns.
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