Question

The random variable is normally distributed with parameters m and o. Find Pła s&s ), P{$\>B}. Put down the 20-rule, give its geometrical and practical interpretation At

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Answer 1

The reandem ve a om variable parameters & is distribuced Normally naar het m and an VaR in. & NN (M, 92) % 2= 8. m. ~N(0,1) ie.2: E-m: ~ N(0,1) Go P[ x 4 & 4 P1 = P[<<m< & -m + Ba mh] =P[..2€ per on ] :P[10242 € ] :P[24245] - PL-16 2 2 3 1 | (4) + (-) 10.33)- (-1) 8.6293-§ 1-$(1)}

的AI, = = 0-6243-1+ (1) 1.0-62 93 -1 + 0.8473 : 1.4106 -1 : 0406 (Au). 三y [11P] ::- PCI 1<b] - - - P/-== =+] |- [ 2 3 4 =“/ : : - FT-3-2 g = =] : : 1- PT-342-5] --= 至()- (-5) : : 1-5 至(03) - [ {- 至 [f-6 1)]; --本C-661) - (0.33)+2 3-( 0.4525+ 0-6293) = 0.4182 (no) |

L T -9413517414219 V LLL iniy 0416001 990 951 1960 43190 Put docou the 20 vence:- The 20 veule can be stated as an empirical seule is a statistical veule which states that for a normal distribution, almost 95% of and data falls within a standard deviations (deuoled by a) of the mean (deuoled by m). Broken down the empivical rule shows. that 68% falls with first standared. deviation CMI), 95% within the first and. two standard deviation (maaa) 95% ESSE RAWD . M-20 4-0 u Meon M+201 Here value of m-20 = 2- (883) = -4 M+20 = 2 + (2x3) = 8 ie. 96). Of the data au'll fall between. - 4 and 8