16.322 Stochastic Estimation and Control, Fall 2004 Prof vander Velde However, for values of k much smaller or larger than u, the probability becomes all sma The normal distribution Outline 1. Describe the common use of the normal distribution 2. The practical employment of the Central Limit Therorem 3. Relation to tabulated functions Normal distribution function Normal error function Complementary error function 1. Describe the common use of the normal distribution Normally distributed variables appear repeatedly in physical situations Voltage across the plate of a vacuum tub angle trac Atmospheric gust velocity Wave height in the open sea 2. The practical employment of the Central limit Therorem X(i=1, 2,, n)are independent random variables Define the sum of these Xi as ∑ s=∑X Then under the condition lim -A=0 9/30/2004955AM Page 3 of 1016.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde 9/30/2004 9:55 AM Page 3 of 10 However, for values of k much smaller or larger than µ , the probability becomes small. The Normal Distribution Outline: 1. Describe the common use of the normal distribution 2. The practical employment of the Central Limit Therorem 3. Relation to tabulated functions Normal distribution function Normal error function Complementary error function 1. Describe the common use of the normal distribution Normally distributed variables appear repeatedly in physical situations. • Voltage across the plate of a vacuum tube • Radar angle tracking noise • Atmospheric gust velocity • Wave height in the open sea 2. The practical employment of the Central Limit Therorem ( 1,2,..., ) Xi i n = are independent random variables. Define the sum of these Xi as 2 1 1 2 1 i n i i n i i n S X i S X S X σ σ = = = = = = ∑ ∑ ∑ Then under the condition ( ) 3 1 3 lim 0 i i n S n X i X ii X X β σ β β β →∞ = = = = − ∑