MEDIAN OF THE VARIABLE X. DISTRIBUTED ACCORDING ; TO EXPONENT IAL LAW f(x)= ) 2e^-2x,&xgeqslant 0 0,&xlt 0 IS Select one: 1/2 -1/4 D 1/4 -1/2 (Ln2)/2

To find the median of the variable X, we need to integrate the probability density function (PDF) from 0 to infinity and set it equal to 0.5.The PDF is given by: Integrating the PDF from 0 to infinity: To find the median, we need to find the value of x such that the cumulative distribution function (CDF) is equal to 0.5. The CDF is given by: Since the PDF is 0 for , the CDF is 0 for . Therefore, we only need to consider the integral from 0 to infinity: Setting the CDF equal to 0.5 and solving for x: Therefore, the median of the variable X is .So, the correct answer is .