Log problem_ISI 2010

[rongmon]

Given log(p)x = a and log(q)x = b, the value of log(p/q)x equals
(a) ab/(b - a)
(b) (b - a)/ab
(c) (a - b)/ab
(d) ab/(a - b)

log(p)x stands for log of x with base p. And similarly read log(q)x & log(p/q)x.

[Dreyfus]

[rongmon]

Thanks, great help.

[rongmon]

An unbiased coin is tossed until a head appears. What is the expected number of tosses required?

a. 1

b. 2

c. 4

d. infinity



Thank you.

[Homer Simpson]

i think its infinity. not sure though!

[Shefali]

2tosses..

[Dreyfus]

Take summation of r*(1/2)^r from 1 to infinity.....u'll get 2 as expected no. of tosses

[rongmon]

Could you expand that equation?
Thanks.

[Homer Simpson]

thanks for clearing that up!

[Dreyfus]

Sum= 1/2 + 2*(1/2)^2 + 3*(1/2)^3+....
Multiply whole eq by 2
2Sum= 1+ 2*(1/2) + 3*(1/2)^2+.......
Subtract eq 1 from 2
Sum= 1+(1/2)+(1/2)^2+(1/2)^3+.......
dis series is a gp nd it sum converges to 2

[rongmon]

Thank you!