![]() Because our \(f(x)\) contains the natural exponential function, however, it is easier to take the derivative of the natural log of \(f(x)\) with respect to \(x\) and solve for \(x\) to find the maximum. Using what we know from our calculus studies, to find the point at which the maximum occurs, we must differentiate \(f(x)\) with respect to \(x\) and solve for \(x\) to find the maximum. To be able to apply the methods learned in the lesson to new problems.ġ6.1 - The Distribution and Its Characteristics 16.1 - The Distribution and Its Characteristics.To understand the steps involved in each of the proofs in the lesson.To learn why the Empirical Rule holds true.To learn how to interpret a \(Z\)-value.To investigate the relationship between the standard normal random variable and a chi-square random variable with one degree of freedom.To explore the key properties, such as the moment-generating function, mean and variance, of a normal random variable.To learn how to find the value \(x\) associated with a cumulative normal probability. ![]() This is where you need to put your thinking caps on because 5-sigma doesn’t mean there’s a 1 in 3.5. To learn how to read standard normal probability tables. Five-sigma corresponds to a p-value, or probability, of 3×10 -7, or about 1 in 3.5 million.To learn how to calculate the probability that a normal random variable \(X\) falls between two values \(a\) and \(b\), below a value \(c\), or above a value \(d\).To learn how to transform a normal random variable \(X\) into the standard normal random variable \(Z\).To learn the characteristics of a typical normal curve.To define the probability density function of a normal random variable.Three sigma follows the 68-95-99.7 rule, where 68 of the data falls within one standard deviation of the mean, 95 of the data within two standard deviations of the mean and 99.7 of. Upon completion of this lesson, you should be able to: Also referred to as the three sigma limits or empirical rule, this tool helps calculate the probability that a certain point falls within established parameters.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |