Daily question

[Kanika]

(1)The conditional probability that he knows the answer given that he answered it correctly is mp/mp+1-p.
(2)The expected time that he reaches to safety is 13.33 hours

[Amit Goyal]

by deepti


1 )  p(k/c)=mp/mp+1-p

3) p(both r boys/atleast one of dm is boy)=1/3

     p(both r boys/atleast one of dem is girl)=0

[Khushboo]

1- the conditional prob is p / [ p + (1-p)(1/m) ] = mp / [mp+1-p].

2- Let E be the expected length of time that miner reaches safety.
    then, E = (1/3) (2) + (1/3) (3+E) + (1/3) (5+E)
            E = 2/3 + 1 + 1/3E + 5/3 + 1/3E
            1/3E = 2/3 + 1 + 5/3
            1/3E = 10/3
            E = 10.

3- P[both r boys] / P[atleast one of them is a boy] = 1/3
   
    Prob that both r boys gvn dat atleast one or dem is a girl = 0

[varun]

sorry for late reply

asha's optimal consumption bundle is (15,7)

[varun]

1. p(c/k)=1
  using bayes theorem we get p(k/c)= p.1 / mp+1-p

[varun]

3. p(both are boys / atleast one of them is boy)= 1/3

  p(both boys /atleast one girl) =0

4.p(that both of them have infections after 2 days)=0.5

[Kanika]

Will it be possible for you to post the answer of the past daily questions so that we can chack for the right anwer.Thanks

[Aastha]

Initial bundle is (x*,Y*)= (150,75)
 Stutshy Method; substitution effect=-37.5
                        Income Effect     = -37.5

Hicksian method; substitution effect=-43.93
                        income effect=-31.06
               

[Aastha]

opyimal bundle (X*,Y*)= (15,7)

[ankita]

1)ans is mp/mp+1-p

2) 1/3 and 0

3)  7/16

[Amit Goyal]

21 Feb, 2009

A mine owner derives an income of Rs. 2000 this year and his income falls by Rs. 200 in each following year until no income results. Find the present value of the income stream when the interest is added yearly at
a) 4% p.a.
b) 5% p.a.

[Amit Goyal]

22 - 24 Feb, 2009

Show by means of numerical example that P(B|A)+P(B|A')
a) may be equal to 1;
b) need not be equal to 1.

Given three events A, B and C such that P(A ∩ B ∩ C) ≠ 0, and P(C|A ∩ B) = P(C|B), show that P(A|B ∩ C) = P(A|B)

Show that P(A ∩ B ∩ C) = P(A).P(B).P(C) does not necessarily imply that A, B and C are all pairwise independent.

[Aastha]

present value of the income stream with 4% rate of interest is Rs. 9846.

present value of the income stream with 5% rate of interest is Rs. 9584.

[Amit Goyal]

25-28 Feb, 2009
Income consumption curve for two goods x and y has equation y=2x. What will be the income elasticities for x and y?

A's and B's demand curves for apples are given by
p=20-q (A)
p=5-q/2 (B)
Suppose there are only two consumers in the market. Market Supply function is given by: p=2+Q.
Find the equilibrium quantity and price in the market.

Laxmi is a poor agricultural worker. Her consumption basket comprises three commodities: rice and two vegetables - cabbage and potato. But there are occasionally very hard days when her income is so low that she can afford to buy only rice and no vegetables. However, there never arises a situation when she buys only vegetables and no rice. But when she can afford to buy vegetables, she buys only one vegetable, namely the one that has the lower price per kilogram on that day. Price of each vegetable fluctuates day to day while the price of rice is constant. Write down a suitable utility function that would represent Laxmi’s preference pattern. Explain your answer.

A person wants to sell his labor and spend his income entirely on the consumption of good G. His utility function is given by u= (1/2)log(G)+(3/4)log(L) where L is number of leisure hours. Maximum number of hours available in a day = 10 i.e. if he works for x hours then his leisure hours equal 10-x. Give the supply curve of labor. Assume that price of G=1.

[Khushboo]

1- Present value when interest rate is 4% =
    2000 + 1800/(1.04) + 1600/sq(1.04) + 1400/cube(1.04) + ............. + 200/(1.04)power9

    = Rs 9824.05

     Present value when interest rate is 5% =
    2000 + 1800/(1.05) + 1600/sq(1.05) + 1400/cube(1.05) + ............. + 200/(1.05)power9

    = Rs 9569.15

   

[Khushboo]

1(a) P(B|A)+P(B|A') = 1, for example
     A coin is tossed twice. Let A and B be d events given by
     A - the first toss is a tail
     B - there is a head on second toss
    n(s) = (H,H) , (H,T) , (T,H) , (T,T)
   so,
      P(B/A) = P(A ∩  B) / P(A) = 1/4 / 2/4 = 1/2
      P(B/A') = 1/4 / 2/4 = 1/2
   therefore,
      P(B|A)+P(B|A') = 1/2 + 1/2 = 1

 (b) P(B|A)+P(B|A')   not be equal to 1, for example
      Suppose a bag contains 5 white and 4 red balls. Two balls r drawn from d bag one after the other without replacement. Let A and B be d events given by
     A - Drawing a white ball in d 1st draw.
     B - Drawing a red ball in d 2nd draw.
 Now,
    P(B/A) = prob of drawing a red ball in 2nd draw given dat a white ball has already been drawn in d 1st draw.

    Since 8 balls r left after drawing a white ball in 1st draw and out of these 8 balls , 5 balls r red.
  so,
  P(B/A) = 4/8
  P(B/A') = 3/8

 therefore, P(B|A)+P(B|A') = 4/8 + 3/8 = 7/8 = 0.875


2- Given three events A, B and C such that P(A ∩ B ∩ C) ≠ 0, and P(C|A ∩ B) = P(C|B), show that P(A|B ∩ C) = P(A|B)

   We knw dat, P(C|A ∩ B) = P(C|B)
                     P(C∩A∩B) / P(A∩B) = P(C∩B) / P(B)
                     P(A∩B∩C) = P(A∩B) P(B∩C) / P(B)
   therefore,
                P(A|B ∩ C) = P(A∩B∩C) / P(B∩C)
                               = P(A∩B) P(B∩C) / P(B)  /  P(B∩C)
                               = P(A∩B) / P(B)
                               = P(A|B)
                                  Hence prooved

       
     


 

[varun]

2- Given three events A, B and C such that P(A ∩ B ∩ C) ≠ 0, and P(C|A ∩ B) = P(C|B), show that P(A|B ∩ C) = P(A|B)

  since  P(C|A ∩ B) = P(C|B)
                     P(C∩A∩B) / P(A∩B) = P(C∩B) / P(B)
                     P(A∩B∩C) = P(A∩B) P(B∩C) / P(B)      .....(1)
   therefore,
                P(A|B ∩ C) = P(A∩B∩C) / P(B∩C)
                               = P(A∩B) P(B∩C) / P(B)  /  P(B∩C) .......(from 1)
                               = P(A∩B) / P(B)
                               = P(A|B)

                                 

[deepti]

(a)two dice r thrown.let A  be d event dat 4 comes on first die

let B  d evnt dat sum is 6.

A={(4,!) (4,2) (4,3) (4,4) (4,5) (4,6)}
B={4,2) (2 4) (5,1) (1 5) (3 3)}

P(B/A)=1/6

P(B/ACOMPLEMENT)=2/15

p(b/a)+p(b/a cmplmnt) is nt equal to 1


(b) suppose a coin and a die r thrown.let A  be d evnt dat head comes up

let  B be d evnt dat eve no comes up.

sample space=h1,h2,h3,h4,h5,h6,t1,t2,t3,t4,t5,t6


p(b/a)=1/2

p(b/acmplemnt)=1/2

p(b/a)+p(b/a cmplmnt)=1

[deepti]

1) INCM ELASTICITY OF X AND Y IS 1

2) EQUILIBRIUM PRICE IS 8 AND QTY IS 6

3) UTILITY (R,P,C)=RP+RC+R

[Khushboo]

1- Income consumption curve for two goods x and y has equation y=2x. What will be the income elasticities for x and y?

 Income elasticity for x is 1 and Income elasticity for Y is also be 1.


2- The equilibrium quantity and price in the market is 6 and Rs 8.


3- utility function that would represent Laxmi’s preference pattern is:
    u( R,C,P ) = RC + RP + R