Question

Theoretical Exercise 4.12. A random walk $S_n$ consists of sums of successive steps $X_i$, each of which can be $\pm 1$ with probability $p$ for $X_i = 1$ such that $S_n = \sum_{i=1}^n X_i$. Show that $(S_n + n)/2$ is binomially distributed and work out its mean and variance.

          Theoretical Exercise
4.12. A random walk $S_n$ consists of sums of successive
steps $X_i$, each of which can be $\pm 1$ with probability $p$ for
$X_i = 1$ such that $S_n = \sum_{i=1}^n X_i$. Show that $(S_n + n)/2$ is
binomially distributed and work out its mean and variance.

Theoretical Exercise
4.12. A random walk Sn consists of sums of successive
steps Xi, each of which can be ± 1 with probability p for
Xi = 1 such that Sn = ∑i=1^n Xi. Show that (Sn + n)/2 is
binomially distributed and work out its mean and variance.

Added by Mar-A A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shyam P

04/23/2022

Step 1

We have a random walk $S_n = \sum_{i=1}^n X_i$ where each step $X_i$ can be either +1 (with probability p) or -1 (with probability 1-p). Show more…

Show all steps

Thanks for your feedback!

Please give me the answer clearly Theoretical Exercise 4.12.A random walk Sn consists of sums of successive steps Xi, each of which can be 1 with probability p for Xi= 1 such that Sn = E=1Xi. Show that (Sn + n)/2 is binomially distributed and work out its mean and variance