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# Determine the cumulative distribution function of a binomial random variable with n=3 and p=1/4.

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Determine the probability mass function of the random variable with binomial distributions with the parameters $n = 3, \ p=0.25$:

$\begin{equation*} f(x) = \dbinom{3}{x}0.25^x \times 0.75^{3-x}, \ \ x = 0, \ 1, \ 2, \ 3 \end{equation*}$

Calculate the cdf:

$F(x) = \begin{cases} 0 & x < 0 \\ f(0) = 0.421875 & 0 \leq x < 1 \\ 0.421875+f(1) = 0.84375 & 1 \leq x < 2 \\ 0.84375 + f(2) = 0.984375 & 2 \leq x < 3 \\ 1 & x \geq 3 \end{cases}$

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