Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

Posted by duck on Apr 07, 2010; 8:02am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4863585.html

Q2 >>> its 2

Let "x" indicate the number of tosses of the coin

The number of tosses of the coin would be

    * 1 if a head appears on the 1st throw
    * 2 if a tail appears on the 1st throw and a head appears on the 2nd throw
    * 3 if a tail appears on the 1st 2nd throws and a head appears on the 3rd throw
    * ... ... ... and so on..

We know, In a single throw with a coin, Probability of:

P(H) = 1/2 = P(T)

Now,  probablity distribution would be

   
       x         P(X=x)                     x*P

      1            1/2                       1/2
      2          ( 1/2 ) ^2                2 * ( 1/2 ) ^2
      3          ( 1/2 ) ^3                3 * ( 1/2 ) ^3
      .                .                          .
      .                .                          .
      .                .                          .
      .                .                          .

Therefore , expected number of tosses = summation x*P =  1/2 +  2 * ( 1/2 ) ^2  +    3 * ( 1/2 ) ^3 +...

solving the above >> we get expected no = 2