Worked Example

Example 5: CDF Deduction

Binomial pmf (n=4, p=0.5)

Given the probability function f(x) = \frac{\binom{4}{x}}{16} for x \in \{0, 1, 2, 3, 4\}: (a) Find the cumulative distribution function (CDF) of the r.v. X. (b) Find f(2) using the CDF.

Solution

Step 1 of 3

Step 1

Compute the cumulative distribution function $F(x)$ for all values.

Cumulative sums: 1/16, 1/16+4/16, ..., 16/16

info

Perfect! Each CDF value is the cumulative sum: $F(0)=f(0)=\frac{1}{16}$, $F(1)=f(0)+f(1)=\frac{5}{16}$, $F(2)=\frac{1+4+6}{16}=\frac{11}{16}$, etc.