Advances in Genetics, Vol. 1 by M. Demerec (Ed.)

By M. Demerec (Ed.)

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Versicolor within each size bin (n = 50 petals total). sample of petals, we will not observe the same numbers again. The statistical model tries to say something useful about the sample of numbers, without trying to say exactly what those numbers will be. The Gaussian distribution describes (quantitatively) the way the numbers will tend to behave. This is the essence of statistical modeling. DEEP THOUGHTS ABOUT THE GAUSSIAN DISTRIBUTION The distribution was probably first introduced as an easier way to calculate binomial probabilities, which were needed for predicting the outcome of dice games, which were very popular even back in 1738.

On the right, thermometer readings (T1, T2, T3, …) decreasing according to Newton’s law of cooling describe the equilibration of the temperature of an object whose temperature is greater than its surroundings (T0). 1, left panel). A series of measurements of a flying (or falling) object can be replaced by the starting position and velocity of the object, along with a simple mathematical formula (second derivative of the position is proportional to mass over distance squared), and some common parameters that are shared for most flying (or falling) objects.

Derive Bayes’ theorem. 2. Show that Bayes’ theorem is true even if the two events are independent. 3. , the sum of all possible observations is 1). ) 4. It’s not quite true that –∞ to ∞ is the only range for which the Gaussian integral can be evaluated. There is one other range. What is it, and what’s the value of the integral? ) 5. Explain why n + m + 1 divided by 2 is the expected average rank in the WMW test. ) Statistical Modeling ◾ 41 6. Use the central limit theorem to argue that the null distribution of the WMW test statistic should be Gaussian.

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