Examples with Normal Distributions

FunLog++ message	Explanation
`moments([0,1]) < X`	Gauss normal distribution N(0,1) with mean 0 and variance 1 is represented in FunLog++ as `moments([0,1]`. We now can test which part of the area under curve is below some value X. The FunLog++ interpreter calculates the probability for an X value according to the probability density function of normal distributions. The message `moments([0,1]<X`relates a stochastic distribution (with mean 0 and variance 1) to some value X. The FunLog++ interpreter evaluates this term and generates an appropriate probability depending on X. Click on the message link to see the result of this calculation which is displayed. `if X = 0 then area = 0.5000` `if X = 1 then area = 0.8432` `if X = 2 then area = 0.9800` `if X = 3 then area = 0.9992`
`moments([0,1])` `- moments([0,1])`	This message denotes the difference of two stochastic variables which is displayed as `(moments([0,2]))`.
`X = moments([0,1]),` `X - X`	This message denotes the same difference like in the previous example but now FunLog++ can recognize, that the two operands are identical. Thus the result is displayed as `0`.

Last modification: B. Pohl 22.August 2000 / 07.November 2000