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The F-variate, named after the statistician Ronald Fisher, crops up in statistics in the analysis of variance (amongst other things).
Suppose you have a bivariate normal distribution. You calculate the sums of squares of the dependent variable that can be explained by regression and a residual sum of squares.
Under the null hypothesis that there is no linear regression between the two variables (of the bivariate distribution), the ratio of the regression sum of squares divided by the residual sum of squares is distributed as an F-variate.
There is a lot more to it, but not something that is easy to explain in this manner - particularly when I do not know your knowledge level.
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What the deference between variable and variate?
A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values.
Can the standard normal variate in normal distributions be negative?
About half the time.
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The number of times a variate is observed in a population is the frequency of that variate. For example if plant length is under observation and in a population of plants having one meter length is measured 15 ; the frequency of 1 m tall plants will be 15.
What is continuous variate?
A variable defined on a continuous interval as opposed to one that can take only discrete values.
What is the product rule for derivatives?
If this is a homework assignment, please consider trying to answer it yourself first, otherwise the value of the reinforcement of the lesson offered by the assignment will be lost on you.The product rule for deriviatives is d/dx f(x)g(x) = g(x) d/dx f(x) + f(x) d/dx g(x).Think about it. You treat this as two partial deriviatives, one with f(x) and the other with g(x). In each case, the alternate is treated as constant, and can be pulled out of the deriviative. Yes, I know, partial deriviatives is part of multi-variate calculus, which is second year, but I'll leave the first year proof to the reader.
