Show that the F distribution with 4 and 4 degrees offreedom is given byg(f) =$6f(1 + f)−4 for f > 00 elsewhere and use this density to find the probability that for inde-pendent random samples of size n = 5 from normal pop-ulations with the same variance, S2 1/S22 will take on a value less than 12 or greater than 2.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
freedom is given by
g(f) =
$
6f(1 + f)−4 for f > 0
0 elsewhere
pendent random
ulations with the same variance, S2
2 will take on a value
2 or greater than 2.
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