UCS410 Thapar Institute of Engineering and Technology (TIET) Solution
Probability and Statistics(UCS410) Exp. sheet 07 (Chi-square, t-distribution, F-distribution) ———————————————————————————————————————————— (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.