Question

Show that the function on the right is a probability density function on [0, 0); then find the indicated probabilities. if O sxs 2 f(x) = 128 5, if x > 2 375, Choose the procedure below that you would use to show that f(x) is a probability density function on [0, 0). O A. Show that f(x) 20 on the interval and that the integral of f(x) from 0 to o equals 1. B. Show that f(x) > 0 on the interval and that the integral of f(x) from - to o equals 0. O C. Show that f(x)20 on the interval and that the integral of f(x) from 0 to o equals 0. OD. Show that f(x) > 0 on the interval and that the integral of f(x) from - to wo equals 1. оо Perform the procedure to show that f(x) is a probability density function on [0, 0). Is f(x) a probability density function? O A. No OB. Yes Find P(o sxs2). P(Osxs 2)= (Type an integer or a simplified fraction.) Find P(x22). P(x22)= (Type an integer or a simplified fraction.) Find P(15x83). P(1sx53) = (Round to four decimal places as needed.)

Answer 1

Solution: Here concept of probability density function is used.

Solution if o x4 2 flx) 12 128 if 325 Phobability danaity fimetion show that flx) is a show thot To Lo,) the in terva would f(x)o we om euals 1 that integral f(x) from 0 the to o and Huna is option (A) correct Now, and 128 3x5 interval o,) . flx) o in the .. that shall show 1 We fla). dx 2 28 dx dx fla). dx 3 5 12 2 0 ** # 2 128 12 4 3 0 2 4 128 1 2 + O 3 2. 4x 2 128 + 3 3 64 + 3 1

1 flx). dx integrad fla) fm there fore, Since flx)2o eual to O to ao is and Phobability dunaity fla) is 1 fine tion "Yes is Answr 2 3 P(02) flx) dx 2 dx 1 2 3 PlOsa) P(Z22) 12 8 f(x)-dx dx 3 5 2 రా 5dx 128 128 44 3 2 2. -12 8 4x24 -128 64 Plx22)

3 P 3) f(x). dx 3 2 3 dx 128 12 3 x5 2 3 2 128 44 2 12 3 12.8 12 4 4x34 3 4 x 2 128-65) 12 3 5184 130 + 243 16 3295 388 8 II II II