Question

24.3. Exercises 317 : 24.19. Suppose a density fx(2) increases linearly from (16,0) to Exercise 24.1 (24,1/4). a. Find the CDF of X. What is the value of a so that PCX al = 0.752

24-19

Answer 1

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434,1) This stroight line denotes the PDF of the given Random Variable we find the PDF by constructing the equation 10,1t.. ....2124, 1) (0,0) 0 (16, 2 4,0) of the straight line. x-16 24-16 => y = I 4X8 (-16) - where y = fx (2). they fx(x) = { 2 / 2 - £ , 1650224 me Lo o , if thur, F(n)=r x<16 . (85) dt , if x 6 [16, 24) if x7,24 Now, wowo, § 23 - #.) felt - 2) (47 Pla - e +4 i f(x) = co ,n<16 +4, 2€ [16,24) *2-4

1) P(xy) = 0.75 1. ) - PCX30) S075 | PCX 4 4) = 0 1 57 교 슈 6 > -- 320 + (=I) -o 32a t 16X15-0" -) a - 320 + 240 =0 키 2 - 20a -12a + 20112=0 ㅕ (A-20) (a-12) =0. Now, the CDF F is o below it, this, we do not consider a=12, 규교 교과 our desired value is. a=20, Thus, 1. Pl*20) = 6,755