Notes on Random Processes

Unfortunately, there’s no simple formula for this integral. Instead, tables or numerical approximation routines are used to evaluate it. The normal distribution has a characteristic bell shaped pdf. The center of the bell is at x = μ, and the parameter σ controls the width of the bell. The particular case in which μ = 0, and σ = 1 is referred to as the standard normal random variable. The letter Z is typically used for the standard normal random variable. Figure 1 shows the pdf of the standard normal. The expected value of a random variable X is