To find the expected value and median of the probability density function f(x) = 1/2e^-x/2 for x > 0, one must first ensure that the function is normalized, meaning its integral equals 1. The expected value for a continuous random variable is calculated using the integral of x multiplied by the probability density function over its range. The median is the value that divides the probability distribution into two equal halves, typically found by solving the cumulative distribution function for 0.5. Understanding these definitions is crucial for accurately determining the expected value and median. Proper normalization and integration techniques are essential in this process.
