Question

Let X be a binomial random variable with parameters n and p. Show that the PMF of X can be computed by starting with $p_X(0) = (1 - p)^n$, and by using the recursive formula $p_X(k + 1) = frac{p}{1 - p} cdot frac{n - k}{k + 1} cdot p_X(k)$, where $k = 0, 1, dots, n - 1$.

          Let X be a binomial random variable with parameters n and p. Show that the PMF of X can be computed by starting with $p_X(0) = (1 - p)^n$, and by using the recursive formula
$p_X(k + 1) = frac{p}{1 - p} cdot frac{n - k}{k + 1} cdot p_X(k)$, 
where $k = 0, 1, dots, n - 1$.

$Let X be a binomial random variable with parameters n and p. Show that the PMF of X can be computed by starting with pX(0) = (1 - p)^n, and by using the recursive formula pX(k + 1) = fracp1 - p cdot fracn - kk + 1 cdot pX(k), where k = 0, 1, dots, n - 1.$

Added by Jamie M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Rosina Dapaah

02/06/2022

Step 1

** Show more…

Show all steps

Thanks for your feedback!

Let X be binomial random variable with parameters n and p. Show that the PMF of X can be computed by starting with p_X(0) = (1 - p)^n, and by using the recursive formula p_X(k + 1) = p/(1 - p) * (n - k)/(k + 1) * p_X(k), where k = 0, 1, ..., n - 1