Probability density function of a random variable X is given below \[{\text{f}}\left( {\text{x}} \right) = \left[ {\begin{array}{*{20}{c}} {0.25}&{{\text{if }}1 \leqslant {\text{x}} \geqslant 5} \\ 0&{{\text{otherwise}}} \end{array}} \right]\,{\text{P}}\left( {{\text{X}} \leqslant 4} \right)\] A. $$\frac{3}{4}$$ B. $$\frac{1}{2}$$ C. $$\frac{1}{4}$$ D. $$\frac{1}{8}$$

The correct answer is $\boxed{\frac{1}{4}}$.

The probability density function (PDF) of a random variable $X$ is a function that gives the probability of $X$ taking on a value in a small interval around a given value. The PDF is often denoted by $f_X(x)$.

In this case, the PDF is given by

$$f_X(x) = \begin{cases} 0.25 & \text{if } 1 \leq x \leq 5 \\ 0 & \text{otherwise} \end{cases}$$

The probability that $X$ is less than or equal to $4$ is given by

$$P(X \leq 4) = \int_1^4 f_X(x) dx = \int_1^4 0.25 dx = \frac{1}{4}$$

Therefore, the correct answer is $\boxed{\frac{1}{4}}$.

The other options are incorrect because they do not represent the probability that $X$ is less than or equal to $4$.