DSE DOUBT

[Sris]

Three players A,B and C take turns playing a game as follows.A and B play in the first round.The winner plays C in d second round,while d loser sits out.The winner of the second round plays the persons who was sitting out.The game continues in this fashion ,with the winner of the current round playing the next round    with the person who sits out in the current round.The game ends when a player wins twice in sucession,this player is declared the winner.For any of d rounds,assume that d two players playing the round each have a probability 1/2 of winning the round,regardless of how the past rounds were won or lost.

1. the prob. that A wins is
a)5/14
b)1/2
c)3/7
d)7/16

2.the probability that C WINS the contest is
a)1/7
b)1/5
c)1/8
d)2/7


this is from dse 2006...plz help...

[naren]

1///   possible game sequence are-  (a)  AB, AC or  AB, CA, BC, AB, AC or similarly cont.......
                                                           probability= 1/2^2 +1/2^5 + .......=2/7
                                                   (b) BA, CB, AC, AB or BA, CB, AC, BA, CB, AC, AB or .........
                                                          probability= 1/2^4 + 1/2^7 +.........=1/14
                                                        so total prob= 2/7 + 1/14 = 5/14
     NOTE-in game sequence FIRST letter indicate WINNING of that player
             for e.g- AB, AC  means A wins first game and also second game.

2///  possible game sequence are-  (a) AB, CA, CB or AB, CA, BC, AB, CA, CB or .............
                                                      prob= 1/2^3 + 1/2^6 + ..........=1/7
                                                  (b) BA, CB, CA or BA, CB, AC, BA, CB, CA or ............
                                                      prob= 1/2^3 + 1/2^6 + ........=1/7
                                                   so total prob=1/7 + 1/7 =2/7

[Sris]

omg...so many cases...

thank u naren...

[Sris]

suppose a real valued function f is defined for all real numbers except 0. it also satisfies the following condition...f(xy)= f(x)+f(y) for all x,y in d domain.consider the statements...

i)  f(1)=f(-1)=0

ii)    f(x)=f(-x) for every x

which of the following statements is true?


plz help...

[Dreyfus]

Both statement are true.
For statement 1, consider x=1,y=1, then as per given property of this function:
f(1) = f(1)+f(1)
       =2*f(1)
The above holds iff f(1) =0
Also consider x=-1, y=-1, then
  f(1) = f(-1) + f(-1)
=>0=2*f(-1) <=> f(-1)=0=f(1)
For statement 2, consider x=-x, y=-1
f(-x*-1)=f(-x)+f(-1)
=>f(x)  = f(-x)      (since f(-1)=0)


       

[Sris]

ohh thanku dreyfus....wonderful explanation...

[naren]

hey guys help me out
DSE 2014
suppose  c is a given +ve real no.
The eq lnx=cx^2 must have a
soln if
A) c<1/2e
B) c<1/e
C)c>1/2e
D)c>1/e

[dashabhisek]

[Sris]

hey abhishek...yeh konsa concept hai which u have used....for an equation to have a solution

[dashabhisek]

I solve these kind of questions using maxima minima concepts. Just apply logic. For example, this function is negative at x=0, so if there is a solution then f(x)> 0 for some x>0. So if the function has some solution then the maxima should be positive, I just did like that.

[naren]

dse 2014

A monopolist produces a good with constant marginal cost c>=0. The monopolist sells the entire output to a consumer whose utility consuming x units of good is theta*sprt(x)-t, where t is payment made by consumer to monopolist. If Consumer does not buy from monopolist, she gets 0 utility. Monopolist profit is
A) theta/4c
B) theta^2/4c
C) c*theta^2
D) c*theta/2

[Sris]

suppose there are three profit maximizing firms who produce a homogeneous good at zero cost. the inverse dd function for this good is p= 1-q where p=price and q =total output produced by these firms.suppose the firms choose their output sequentially ,with firm 1 choosing q1 first, firm 2 choosing q2 next(having seen q1) and firm 3 chooses last (having seen q1 and q2 )

if these firms behave rationally (ie act so as to maximize profits) given their info and anticipate rational behaviour by their rivals,then what will the outputs chosen by the firms.

(this is stakelberg with an extra sequential follower thrown in)

PLZ HELPPPP.....

[Sris]

NO DOUBT IN THIS QUESTION...

IF SOMEONE ELSE HAS A DOUBT IN THIS QUESTION STAKELBERG ONE ..PLZ ASK ME I HAVE SOLVED IT

[Sris]

OK I HAVE ANOTHER DOUBT...ITS FROM DSE 2005 SUBJECTIVE Q3 PART (A)...RURAL URBAN ONE...PLZ HELP...


ITS A LONG ONE...I AM NOT ABLE TO COPY THE QUESTION HERE

JUST HELP ME SOLVE (b) part of it...reliance one

[Sris]

suppose there are two states...today n tommorow. tommorow may b state 1 or state 2 or state 3.there are 3 securities n their prices tommorow in various states are as (1,1,1) for security 1..for security 2 it is (1,3,-1)..n for security 3 its (-2,-1,0)..price today of these securities are 4,1,5 respectively.now suppose there is a fourth security whose price tomorrow is (3,1,4).what should be the price of fourth security today so that there are no arbitrage possibilities??
    plz solve this one tooo...

[honey2901]

Yeah can you please explain the same in lucid manner.

Regards

[honey2901]

yes boss can you please explain.

[Sris]

stakelberg one?

[Sris]

plz someone reply to my queries...

[Sris]

plz someone help me....i have posted two queries...