Module -1
11 8) Six dice are thrown 729 times. How many limes do you expect a least three dice (0

show | or 2?
b) Derive the Tonnuta for mean und variances of Poisson distribution
12 a) Asandom variable X ലിയ the values -3, -2, -1,0,1 2,3 serch tha: 00) = 1५०००) =
00൭) and 500൧൭552) = 80.3) = 2൮൦...) = P(X@!) = 7002) = 70൫൮). Obtain
the probability mass function snd distribution function of 3.
0200031: 71
b) The joint piobehiljty distribution ofX Mid Y is given by, 1४ 0) 5 2 (2x +
X =0.1.2a0d =
(1) Findthc marginal distHbuLions ol'x md ‏لا‎
‎(ii) Are X and Y "Klepeadem mndomvariables,
Module -2

اہ

17 3) Suppase the diameter al héi#t (in) or or cenaid cype is normally 7 ५5110५60 ‏۰.۷۱]۳٭‎ 8.5 abd
standnrd devinion 2.g.(i) Wbei is Ihc proiibilicy that (1001277067 randomly selecled will d' 0
inn (ii) Whel 15 the prok»bilit-y Ole diameter a randomly 56161166 ace grill 20 infi (iii) Whal

is the probability the diameter OF a randomly bc bemcca 31൩. and 10 in.?

b) The time Will mm having n be lesel is 7a ta_ndom variable having wia mean 50 days.
Find ihc probabiliLies Lhal such ‏ل‎ amen hzvc to bc in ‏مقطا‎ 20 days. no' have lobe teset in

al days.
Tie joini density mn:tionof2 eontinuodsmndom uu-iHble X and Y
CXyO 4۱۷ < otherwise

Find Lhe value of cons-tun

(ii) Find F (X23,
(iii) Findthe de-asily of X.
lire Lime of a eenain brand or cube light may be ട്ട random variable
a wiLh mean 1200 and snudatd devietioa 250 theoremadind Wing (வாமி 090
,eptobabiliry [he average lire 'unc of 6005 £60 lights ബാ 1250
Module ்‌

Let A E Sin randdm ५808४ Indepentterttnormally distributed
Show '೧೩' XO) is WSS.
XO) = ccc Vi-here A and are constan and 0 dLstTibutwd ९५९ 27], ९6९९४
correlation function and Powgr

1 7
ண்டி ளி எக. action and Power Speciral