Probability and Statistics(UCS410) Exp. sheet 07 (Chi-square, t-distribution, F-distribution)
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(1) Use the rt(n,df) function in r to investigate the t-distribution for n = 100 and df = n − 1 and plot the histogram for the same.
(2) Use the rchisq(n,df) function in r to investigate the chi-square distribution with n = 100 and df = 2,10,25.
(3) Generate a vector of 100 values between -6 and 6. Use the dt() function in r to find the values of a t-distribution given a random variable x and degrees of freedom 1,4,10,30. Using these values plot the density function for students t-distribution with degrees of freedom 30. Also shows a comparison of probability density functions having different degrees of freedom (1,4,10,30).
(4) Write a r-code
(i) To find the 95th percentile of the F-distribution with (10,20) degrees of freedom.
(ii) To calculate the area under the curve for the interval [0,1.5] and the interval [1.5,+∞) of a F-curve with v1 = 10 and v2 = 20 (USE pf()).
(iii) To calculate the quantile for a given area (= probability) under the curve for a F-curve with v1 = 10 and v2 = 20 that corresponds to q = 0.25,0.5,0.75 and 0.999. (use the qf())
(iv) To generate 1000 random values from the F-distribution with v1 = 10 and v2 = 20 (use rf())and plot a histogram.
