Question

3. The discrete random variable X has the following probability distribution: IX 13 18 20 24 27 P(x) 0.22 0.25 0.20 0.17 0.16 a. P(18) b. P(X > 18). C. P(X s 18). d. The mean u of X. e. The standard deviation o of X.

Answer 1

Answer The discrete ng probability random variable x has followi- distribution. 1 xea P(x)_ 13 0.22 18 0.25 20 0.20 24 v 27 0.17 0.16 PC 18 ) = P(x=18) = 0.25 w P(18) = 0.25 p(x>18) P(x220) + P(x=24) + P(x227). 0.20 +0.17 + 0.16 - PX>18) 0.53 C) PCX $ 18) - = = PC X=-13) +PCX218) 0.22 +0:25 0.47. mean lof X = ECX) M= E(X) = 5 x P(x) = 13 (0.22)+ 1810.25 )+ 2010.20)+3460.17)| +27 (0:16) 19.76 _ __

To complete the standard deviation of x. First we compute its variance (62) ; variance of x Ir2 -ECx2) - TE .: E(X2)= 5 x2.P(x=x) 5 (132) (0.22) +(182) (0.25) +(202) (0.20) +(242)(0.17) + (272) (0.16). = 412.74 1} variance of x=02: 412.74 – (19.76)* 9:02= E(X2) - TECx)]2 = 22.2824 .". standard deviation of x = 0 = 102 __= 222824 = 4.7204 .: Os 4.7204