The ratio of the variance of two samples s12s22 of different

The ratio of the variance of two samples (s_1^2/s_2^2) of different sizes (n_1=3,n_2=6) but created by successive observation of the same random variable, has an F_2,5 probability distribution function. What is probability that the ratio of the such samples variances would be between 0.0518 and 8.43?

Solution

As df1 = 2, df2 = 5, then

P(F<0.0518) = 0.049978489
P(F < 8.43) = 0.974979291

Thus,

P(0.0518 < F < 8.43) = 0.925000802 [ANSWER]