oa

b) The dine required (0 repair a machine டீ exponentially desietbuled with a parameter
0.5. What gs the probuhility that ४ repair யாடி exceeds 2 hours? Whal is the 8
conditinnal probability thal a repair time iakes ‏اج ارہ‎ 10 hours நே thal its
(luration exceeds 9 hours?

probnhiliLy nai
probabililY | 21 repair [110८

H2MONLA 204052॥॥5

PART B two
4 3) A random s.rnple or sue 100 js lakcn from populaGon meat' is 60 an' vutiance LS 400. Using

Cctucel Theorem. with whal mobaSilily canwc 7? assen mean sample differ Crom SO

by 'nor: 4?
0) The join! disueibulinotrwo nndom vanables X and Y 15 giueLity
அட and |, 2, Find ehe mgrgiul distributions or X and
5 Consider due rendom process X(c) p) whcre rp

distribuzed random veci.ble in (—m 1) . Check whelhec Lhe ptxcss 5LnLioa,,ry_

h) powerspectra] pmcess whose NulDeqmi:|stinn - where 0. Also find Lhe
power of ehe process. 6 a) The joint pmbabiliry dcnsiry of. Svo-dimeasional nndom
variable (X, Y)

js givenby 52, 1.
compo’. (i) Ptx >

0) [X (t) = ACOS r is ru_ndorn process where A and independen' mndom veriablcs

roilowing delribuGon Ittean 0 and variance . Ekannne wheLhec 'X(t)} is
5A.on.ryPART C

७) ^ syslem 1௦ bc Markovian [he
Ol- die current in—sage Lhe us given by [he inalrix
0.2 0.3 0.5
0.2 0.7 0.3 0.3], Find ൩:

0.6 0.3 0.1 enne
next messa*

initial distribulion P(O) (0.7, 0.2, 0.1).