Question

Verify that the following function is a probability mass function, and determine the requested probabilities. f(x) = x = 0,1,2,3,4 Is the function a probability mass function? 6x+4 80 Give exact answers in form of fraction. (a) PIX =4) - (b) P(X s 1) - (c) P(2 s X < 4) = (d) PCX > -10) -

Answer 1

YES

a) answer - . 35

b) ans - . 175

c) answer - .475

d) answer - 1
P ) SOLUTION probability mass function f9c) at y=0,1,2,3,4. (Outcomes) 6x + 4 80 If this is probability mass function.in If and ONLY If x=4 Ef(x) =1 =1 aute 2 4 x o point LOUT comet 3 222 22 10 4. 80 16 80 28 80 80 pro babi +f6x) lity 6xot4 6x144 2 flo) ful) =Ş 10 80 80 f(2) 6x2 + 4 16 = 0x3+4 f(3) = 22 80 ) 80 8 80 80 f (4) 684+4 28 80. 80 + 10 80 + 16 80 + 22 80 80 Žfory=f(0) + f(l) + f(2)+44) + f(4) = 4 x=1 t 28 =1 Yes function is probability mass function 6x4+4 (9) ANS f(x=4) plot =4) 28 -10-35 80 ANS 28 80 CS Scanned with CamScanner

(12) (6) ANS PLX (1) Rok f(I=0) + f(1=1) Ex174 Exot4 노 10 + .0.175 t 86 80 8o 80 As #(252) + f(2-3) P(2<x<4) (C) ANS 6x2 + 4 6x3+4 - + go 8 16 22 = f =(0.475 Paris 86 80 CS Scanned with CamScanner

(d) Ans P(87-10) = f(150) + f(x=1) + x=2) tf48=3) Africa) 22 4 16 + 10 80 + + + 28 80 =2 80 80 80 CS Scanned with CamScanner