@ Someone plz help! Akshay, Amit sir.....

[H4CK3R]

Kindly help me to find mistake in my approach for the following ques of dse 2014!

Ques: Suppose two restaurants are going to be located at a street that is ten kilometers long. The location of each restaurant will be chosen randomly. What is the probability that they will be located less than five kilometers apart ?

(a) 1/4
(b) 1/2
(c) 3/4
(d) 1/3

I'm getting 3/4 as ans but in solutions provided by dse its 1/4..My approach is as follows:

[Tanya_k]

did not attempt the above question..though your solution seems genuine.

I have a doubt in following ques -

Let Y denote the no. of heads obtained when 3 fair coins are tossed. Then the variance of Z = 4 + 5 Y^2 is

a. 185.5
b. 178.5
c. 187.5
d. none

I'm getting 193.75 (i.e. should be none). DSE ans - c. 187.5

[Amit Goyal]

Ques: Suppose two restaurants are going to be located at a street that is ten kilometers long. The location of each restaurant will be chosen randomly. What is the probability that they will be located less than five kilometers apart ?

(a) 1/4
(b) 1/2
(c) 3/4
(d) 1/3

Answer is 3/4.

Working: Let X denote the location of the first restaurant and Y denote the location of the second. Since X and Y are i.i.d uniform U[0, 10]. the joint density is
f(x, y) = 1/100 for 0 < x < 10, 0< y < 10
= 0 otherwise

Now you can easily find Pr(|X - Y| < 5) = 3/4

[xyz123]

You all should mail your answers to the email ID mentioned in this link
https://docs.google.com/file/d/0Bz5BEtgOHe3ZNGpHRG1lSW9DTzg/edit

It may be wrong, but at least they will recheck

[Amit Goyal]

Let Y denote the no. of heads obtained when 3 fair coins are tossed. Then the variance of Z = 4 + 5 Y^2 is

a. 185.5
b. 178.5
c. 187.5
d. none

V(Z) =  V(4 + 5 Y^2) = 25V(Y^2) = 25(E(Y^4) - (E(Y^2))^2)
Pr(Y=0) = 1/8
Pr(Y=1) = 3/8
Pr(Y=2) = 3/8
Pr(Y=3) = 1/8

E(Y^4) = 0(1/8) + 1(3/8) + 16(3/8) + 81(1/8) = 33/2
E(Y^2) = 0(1/8) + 1(3/8) + 4(3/8) + 9(1/8) = 24/8 = 3

V(Y^2) = 33/2 - 9 = 7.5
V(Z) = 25(7.5) = 187.5

[AnkitKhanna]

  Y.   Prob.   Z.   Z(2)
. 0.    1/8.    4.   16
. 1.    3/8.    9.    81
  2.    3/8.    24.  576
  3.    1/8.    49.  2401

. E(Z)  19
. E(Z2) 548.5
 Var(Z)  548.5 - 361   which is 187.5

[AnkitKhanna]

Q A function f is continuous in [a,b] and diffeerentiable in (a b)
    f'(x) not = to 1 in (a,b)
    A fixed point is defined as a point where
    y = f(y),  how many fixed point will the function have.

    If I take f(x) = x^3 in (1/sqrt(3), infinity) or in (1- iinfinity, -1/sqrt(3))
    we get one fixed point in each interval at x = 1 and -1

    If I take f(x) = x^2 + x + 1 in (0, infinity) or (- infinity, 0)
    I get no fixed points

    Based on first function there is one fixed point in any such interval (a,b), but based on second function there is no fixed point in any such interval (a,b)


Q There are 2 fair coins. First coin is tossed 3 times. X represents number of heads in the 3 tosses.
   After this second coin is tossed X number of times, where Y represents number of heads.
   Find P(X>=2|Y =1)

  I am getting answer as 5/9. Which is not in options , the closest is 11/18 which has been given as the correct answer in key.

[Riya]

Yes Ankit, even I had got 5/9 as the answer which is not in any of the options!! Series 02, right?
Could you pls tell the question no.?

[Akshay Jain]

Even m also getting 5/9
I dont no what is happenning here....so much typos....<smiley image="anim_crazy.gif"/>

[AnkitKhanna]

Yes Riya
I got series 2, but dnt remember the question number and dont have the Q paper

Also are all the answers of econometrics Qs given in the key correct because I ended up attempting all four Qs to increase my attempt and as per the key all of them are wrong.

[Riya]

In this particular question, the answer that we're getting (i.e. 5/9) was not a part of any of the options only. So, I don't think that this is an error of the answer key typo

[Riya]

@ankit - Can't comment upon the ecotrix section as even I don't have the question paper! How did you match your answers without the question paper? Are you sure that they have given 11/18 as the correct option?

[AnkitKhanna]

A friend of mine had sereis 03
Checked answers based on his key i.e 03, but I dont have that Q paper with me now.

and yeah I am sure about the answer being given as 11/18 (And it was closest to 5/9 amongst all options that were given)