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$$\normalsize\ percentile\ x (x≧0)= 1$$ $$\normalsize\ degree\ of\ freedom\ ν1 (ν1＞0) = 2$$ $$\normalsize\ degree\ of\ freedom\ ν2 (ν2＞0) = 1$$
$$● probability\ density\ f\ =0.1924500897298752548364$$ $$● upper\ cumulative\ Q\ =0.57735026918963$$
$$\normalsize F-distribution\ F(x,\nu_1,\nu_2)$$ $$(1) probability\ density$$ $$ \hspace{30px}f(x,\nu_1,\nu_2)={\large\frac{\nu_1^{\frac{\nu_1}{2}}\ \nu_2^{\frac{\nu_2}{2}}}{B(\frac{\nu_1}{2},\frac{\nu_2}{2})}} {\large\frac{x^{\frac{\nu_1}{2}-1}} {\ (\nu_2+\nu_1x)^{\frac{\nu_1+\nu_2}{2}}}}$$ $$(2) lower\ cumulative\ distribution$$ $$\hspace{30px}P(x,\nu_1,\nu_2)={\large\int_{\small 0}^{\small x}}f(t,\nu_1,\nu_2)dt$$
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The F conveyance is the likelihood circulation related with the f measurement. In this exercise, we tell the best way to process an f measurement and how to discover probabilities related with explicit f measurement esteems.
The f Statistic
The f measurement, otherwise called an f esteem, is an arbitrary variable that has a F dispersion. (We talk about the F dissemination in the following segment.)
Here are the means needed to register a f measurement:
Select an arbitrary example of size n1 from a typical populace, having a standard deviation equivalent to σ1.
Select an autonomous arbitrary example of size n2 from a typical populace, having a standard deviation equivalent to σ2.
The f measurement is the proportion of s12/σ12 and s22/σ22.
The accompanying comparable conditions are ordinarily used to process a f measurement:
f = [ s12/σ12 ]/[ s22/σ22 ]
f = [ s12 * σ22 ]/[ s22 * σ12 ]
f = [ Χ21/v1 ]/[ Χ22/v2 ]
f = [ Χ21 * v2 ]/[ Χ22 * v1 ]
where σ1 is the standard deviation of populace 1, s1 is the standard deviation of the example drawn from populace 1, σ2 is the standard deviation of populace 2, s2 is the standard deviation of the example drawn from populace 2, Χ21 is the chi-square measurement for the example drawn from populace 1, v1 is the levels of opportunity for Χ21, Χ22 is the chi-square measurement for the example drawn from populace 2, and v2 is the levels of opportunity for Χ22. Note that levels of opportunity v1 = n1 - 1, and levels of opportunity v2 = n2 - 1.
The conveyance of all potential estimations of the f measurement is called a F dissemination, with v1 = n1 - 1 and v2 = n2 - 1 levels of opportunity.
The bend of the F conveyance relies upon the levels of opportunity, v1 and v2. While portraying a F conveyance, the quantity of levels of opportunity related with the standard deviation in the numerator of the f measurement is constantly expressed first. Consequently, f(5, 9) would allude to a F dispersion with v1 = 5 and v2 = 9 levels of opportunity; though f(9, 5) would allude to a F appropriation with v1 = 9 and v2 = 5 levels of opportunity. Note that the bend spoke to by f(5, 9) would vary from the bend spoke to by f(9, 5).
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A. The F Conveyance Is The Likelihood Circulation Related With The F Measurement. In This Exercise, We Tell The Best Way To Process An F Measurement And How To Discover Probabilities Related With Explicit F Measurement Esteems.