20.

21.

062/21

~ Suppose that the probability of a dry day following a rainy day is 2/3 and that the probability of a rainy

day following a dry day is 1/4. Given that April 15 is a dry day, what is the probability that April 17 is
a rainy day ?
35 13 11

A) in B = 3
) 8 ) हाः ‏کے رہ‎

~ Suppose that customers arrive at a service counter in accordance with a Poisson process with mean

rate of 3 per minute. Then the probability that the interval between two successive arrivals is more
than 1 minute is

A) ० 8) ல ©) 6 D) 2%

. Let the distribution of the number of offsprings in a branching process be geometric with probability

۴

PK = 0 , (= 0, 1, 2,. . ~ , then the probability of ultimate extinction is
1 1 2

A) = ‏رھ‎ 1 ०5 ഉ) 1
3 2 ) 3 )

. Let {X,,, n = 0) be a Markov chain with states | = 0, 1, 2, . . . Let ग =PIXnim = [/ Xm = |] कात

pi 80௩ =K/ Xm = j]- Then which of the following statements is not true ?

1. State jis persistent iff yer =O.
2
2. If state | is transient, then pi” -> 0 ‏وع‎ ०.

3. If K is a transient state and ‏ےا ز‎ an arbitrary state, then lim 9 = 1.
‏مجم‎

4. State jis transient if सी ಆಂ -

A) 1 only 8) 18೧63 C) 2only D) 3 only

The transition probability matrix of a Markov chain {X,, 1 = 1, 2, . . . } having 3 states 1, 2 and 3 is

0.1 0.5 04 ⋅⋅⋅⋅⋅⋅⋅

7-|0.6 0.2 02 and the initial distribution is 70 (0.7 0.2 0.1). Then 06 = 2, Xp = 3, ‏وكا‎ 5 3,
0.3 0.4 3

Xo = മിട

A) 0.0336 B) 0.048 C) 0.279 D) 0.0048

Let T,, be an unbiased and consistent estimator of a parameter 6, then as an estimator of 02, ٥

A) Unbiased and consistent

B) Biased and not consistent
C) Biased and consistent

D) Unbiased and not consistent