Question

6. Suppose that K is a positive constant and f(x) = K sin x is a pdf on 0 < x <T. (a) Find K. (b) Find the cumulative distribution function (cdf) off. (c) Find the inverse cdf off.

Answer 1

Answer:-

constant and flrs= ksin o suppose that K is a positive is a pdf on OL XLĪ. 8 Given if kis found by noting the total probability = 1 "Thus, we get between limits I to a => [-*[* - -]] =) => {x{o - 1}}=1 3) -KE']=r KL1] = 1 k=1 6 Given So, pelif of X is given by f(x)= x ² for Laloo

function (cdf) of Thus, the cumulative distribution f is got as follows: flx) Sady :-[-\s]0 Appliging limits 1 to 20 =f[*-] 1. eq ① Applying limits we get f(x)=1-4 Thus caf is given by. F(x)= 0 for all F(x) = 1-' for for x>1 © Given . The inverse cdf of fis got as follows - f(x) = 1 - f (y) = y The inverse calf of given by o fl-iny