Question

2. Let X be a discrete random variable with the probability function given by f(2) k(x2 – 2x) + 0.2 for x = 0,1, 2, 3. (Note: all answers to the questions below must be fully evaluated.] (a) Find the value of k. (b) Find f(1.38) and F(1.38).

Answer 1

Given probability function of discrete fandom van alle x for kfx?_2x) +0.2 x=0,1,2,3 a) from the function property of a probability we know that E f = 1 N 3 Z nzo k (2²-2x) +0.2 =4 z Kºlo-exy) 70.2 + K (2-271) +0.27 $_*[2_282) +6,2 +_213=243) +0.251 ozt 1[12]+ 0.2 t 10 to 2tk (3) +0.2=L * +34 tot 1 2 k t 0.8 = 1 LA żka to.8 20. * 2 fer-01 te kot

b) so f(1138)=_ [66.22-241223+0,7 OLX(-0.9551) -10% Iffe38) 0.11991 El1:38) = lloc 1:38 P(X=o) + P.(x = 1) fo) t ft) t02-07 +0-2444 tor24€12-24.1+2 0.2Totxe75.biz 02--- OLE01_2 > IF (1.38)=013 if Leto be a rv denoting the no of employeed women have never married Here it is given that 25 of emplo women have been never married 25.11 oyed

ie probability (P)- 25 0.25 you and here we select nw employed women a Binomial then here x will be Rov with parameter no 20 fpo 0:25 xn Bl:20, 0125 and we know that if on Blu, p). then f(x=x) pe (le* snel Here xu B.(20, 0.25) h с. x Ġ so ft tur or fewer) - P(X (2) = P(x50 FP (X=) +P (823) (C2T) (-0.2019 Co to, 6:25) UFO 2012 + 20 2120) (L-0201 ₂ 0.00317_76021141006694 >> P (two or fewer) 20:09126 Ag. 78