SOME SPECIFIC PROBABILITY DISTRIBUTIONS 1. NORMAL RANDOM VARIABLES with mean u and variance a2(abbreviated by x a N[u, 02] if the density function of x is given bb 1. 1. Probability Density Function. The random variable X is said to be normally distribute f(x;μ,a2) The normal probability density function is bell-shaped and symmetric. The figure below shows the probability distribution function for the normal distribution with a u=0 and o=l. The areas between the two lines is 0.68269. This represents the probability that an observation lies within one standard deviation of the mear FIGURE 1. Normal Probability density Function μ=0,SOME SPECIFIC PROBABILITY DISTRIBUTIONS 1. Normal random variables 1.1. Probability Density Function. The random variable X is said to be normally distributed with mean µ and variance σ2 (abbreviated by x ∼ N[µ, σ2] if the density function of x is given by f (x ; µ, σ2) = 1 √ 2πσ2 · e −1 2 ( x−µ σ ) 2 (1) The normal probability density function is bell-shaped and symmetric. The figure below shows the probability distribution function for the normal distribution with a µ = 0 and σ =1. The areas between the two lines is 0.68269. This represents the probability that an observation lies within one standard deviation of the mean. Figure 1. Normal Probability Density Function -1 1 .1 .2 .3 Μ = 0, Σ = 1 Date: August 9, 2004. 1