binomial 61575100000 can bo approiinated to Poisson djst_ribuciou / when n islarge,
p smali andnp = I.
12 a) A gambler plays a game of rolling die "iLh Lhe Collowwg rules-He will Rs 20D if he
throws a 6, but lose Rsv 40 if be hrows4 or ऽ and 1050 R.s. 20 ifhe Lhrews 12 or 3. Find ൩:
expecled value the gambler may gain.

Thcjoir.t dislribuuion 01 (X,is givenby 9) y 1, 2. Then find
‘hS5m2i-ginaJ disltibOtions. Alo, find E(D, E(V).

13 aj In an :xaminamion. or sludenLS got muk5 below 40 and 10% marts above 7 S.
Assuming ‘he marks "re nonna_liy dismbuL:d find, the mean and slandard deviahon
Ot Lhe dismibulion.

೧) Buses 011196 8+1 spaWAed stop al minui:S '-uenal smrring 8 If a 7 passenger arnves 0४८
stop a candom lime is unform]y distmhlled berwwn 8.00 and 8.30 hours, find 10
probability Lhal Lhe passenger Waiu (i) than 6 minus for Lhe bus (ii) 12 minutes for Ihc
bus.

14 0) Adistribmion unlmown mean u*anca 1.5. Use Ccna-al Limit
Thmrem to find, how large a sample should be taken from Lhe distribution in
order [hat the probability that Une sample mean ¥ sample mcan --.vilJ be WiLh in

populaL jaritean is 0.95, [be 0.5 of the
307 of (X, டி 18 given by f(x,y) = (६7५
b) =Q@ TheJOinI 0 > ‏نر >1 ب4 عع‎ > 5
else',;where
Find value of k. Determine marginal pdf OEX and Y- Eva!uale ‏م‎ [Y S
21. Check whether >, ४ ere 17600080007
Module 3

15 2۸ of 20 ilems has me*n 42 and SD 5. Tea whcLher Ihe sampleis from 1
populalion wiLh mean 452 (5% level or significance)

b) "Ihe m:an lire lime or cenain produce is 1800 hrs 170361) of 100 hn. By 7

applying new.’ Lecjuuque, il is claimed ‘he mean 115 hasincreased. 'Eo 8೩3110
claim ப8-10]6 or 56 77೦೮೦15 were taken and it is round LheL the mean 1426 Limc is
1850 Can we suppon Lhe claim nL 1 0/0 level or significance?

प्रे ४ univenily 325 out 01 scudcals ar boys. Does this mformulion suppon 7
1൨ conclusion LhaL majority ot st-udznts in Lhis t_miversity are hoys? (use 5%
Icvcl of significance)

b) Random samples de-gwn from Avo counme gave Collowing relating 10 *heiglll or
೩6011719,

| Country 0

67.25

2.50
‏کس‎ 9 | 1200
‏کا‎ tho difference between 010 means significant? {5% level of significunce}

Is duc differeoce
belween the Incans significaru? level

Module 4
1? 2) The populeioo ot a in die census is as given in Lhe dala_ Est-ilm& ihe 7 population in Ihc
year [996 using h'ck-wm-d 17101701800 ferniula.Year (x) 1961 1971 981 2001
i 1೫! Population

ify): 6