# 5_Continuous distributions - Continuous distributions...

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Continuous distributions Viktor Khanzhyn
Main difference from the discrete distributions Probability function is not showing probabilities directly anymore Probability of X taking a specific value is zero Probabilities are commonly defined for an interval of values X can take Instead of summations use integrals (but we won’t do that!)
Cumulative Cumulative probability function: 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 F X ( x ) P ( X x )
Probability Probability of X taking a value between a and b (a<b) : P X ( a X b ) F X ( b ) F X ( a ) P X ( a X a ) F X ( a ) F X ( a ) 0 P X ( a X b ) P X ( a X b ) P X ( a X b ) P X ( a X b )
Probability density function 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 f X ( x ): f X ( x ) 0 P X ( a X b ) f X ( x ) a b dx
Uniform distribution -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 f X ( x ) 1 b a , a x b 0, else
Uniform distribution Area underneath probability density function equals to 1 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2