GATE CSE
First time here? Checkout the FAQ!
x
+6 votes
555 views

When a coin is tossed, the probability of getting a Head is $p, 0 < p < 1$. Let $N$ be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of $N$ is

  1. $1/p$
  2. $1/(1 - p)$
  3. $1/p^2$
  4. $1/(1 - p^2)$
asked in Probability by Veteran (19.2k points)   | 555 views

1 Answer

+12 votes
Best answer
$E = 1 \times p  + 2 \times (1 - p)p  + 3 \times (1 - p)(1 - p)p  + \dots$

multiply both side with $(1 - p)$ and subtract:

$E - (1 - p)E = 1 \times p  + (1 - p)p + (1 - p)(1 - p)p + \dots$

$  = p /(1 - (1 -p)) = 1$  (because it is now forming a GP)

$=>(1 - 1 + p)E = 1$

$=> E = 1 / p$

 

So, Option (A)...
answered by Loyal (4.7k points)  
selected by
what this anwer means? atleast add some description about which step is taken why? what it implies..? anything? ?
It is an arithmetic geometric progression .That he is solving ...you can see how to solve it


Top Users May 2017
  1. akash.dinkar12

    3152 Points

  2. pawan kumarln

    1616 Points

  3. sh!va

    1580 Points

  4. Arjun

    1336 Points

  5. Devshree Dubey

    1230 Points

  6. Angkit

    1028 Points

  7. Debashish Deka

    1012 Points

  8. Bikram

    972 Points

  9. LeenSharma

    810 Points

  10. srestha

    662 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 May 22 - 28
  1. pawan kumarln

    242 Points

  2. Ahwan

    138 Points

  3. joshi_nitish

    112 Points

  4. jjayantamahata

    104 Points

  5. Arjun

    64 Points


22,725 questions
29,056 answers
65,052 comments
27,566 users