繼續研讀 Applied Statistics for The Behavioral Sciences

• Chapter 4 The Normal Distribution
• 3:50-8:50

常態分布的通用公式與圖形

給定一平均值與一標準差時，可得一特定的常態分布圖形

• The Nature of the Normal Distribution
• The Family of  Normal Distributions
• The normal distribution is not a single distribution but a family of distributions, each of which is determined by its mean and standard deviation.
• Properties of the Normal Distribution 
• A normal distribution is unimodal (having one mode), symmetrical (that is, the left and right halves are mirror images), and bell shaped, with its maximum height at the mean.
• A normal distribution is continuous. There is a value of Y (the height) for every value of X where X is assumed to be a continuous rather than a discrete variable. 
• A normal distribution is asymptotic to the X axis. This means that the farther the curve goes from the mean, the closer it gets to the X axis; but the curve never touches the X axis, no matter how far a particular score is from the mean of the distribution.
• The Standard Normal Distribution
• The standard normal distribution or unit normal distribution is the distribution of normally distributed standard scores with a mean equal to 0 and a standard deviation equal to 1.

常態分配的公式怎麼推導出來?

• 首先用中心極限定理推導出這種分佈的機率密度函數正比於，然後透過平移、縮放，最後調整外圍的那個常數使其包圍著的面積是1而得來。 
• 平移與平均值有關。縮放與標準差有關，使面積為1的係數也與標準差有關。
• 機率論，大數定律