NDA2024MathematicsStatisticsActual
array |c|c|c|c|c|c| _i & 1 & 2 & 3 & & n _i & 1 & 2⁻¹ & 2⁻² & & 2^ -(n-1) array What is the mean of the distribution?
Options
- A2^ n+1 -n+2 2^n-1
- B2^ n+1 -n-2 2^ n-1
- C2^ n+1 -n-2 2^n-1
- D2^ n+1 -n+2 2^n
Correct answer
C. 2^ n+1 -n-2 2^n-1
Step-by-step solution
aligned & f_i=1+ 1 2 + 1 2^2 + + 1 2^ n-1 & f_i= 1- 1 2^n 1- 1 2 = 2^n-1 2^ n-1 aligned aligned Now, Mean & = f_t x_t f_t = 2^ n+1 -n-2 2^ n-1 2^ n-1 2^n-1 & = 2^ n+1 -n-2 2^n-1 aligned