Lecture Probability & statistics: Chapter 6 - Bùi Dương Hải

Lecture "Probability & statistics - Chapter 6: Continuous probability" has contents: Continuous random variable, density function, parameter, uniform distribution, normal distribution, cutoff point. Invite you to consult the content. | Lecture Probability & statistics: Chapter 6 - Bùi Dương Hải Lecture 6. CONTINUOUS PROBABILITY Continuous Random Variable Density Function Parameter Uniform Distribution Normal Distribution Cutoff point [1] Chapter 6. pp. 255 - 294 PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 1 . Continuous Random Variable Continuous Random Variable: uncountable values Available value is one interval: = ( , ) Maybe: = −∞; = +∞ Probability that one point: = =0 Consider Probability at one interval: ( < < ) PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 2 . Density Function Discrete Continuous X X ( , ) Prob. Density ( ) ∑ =1 ∫ =1 p f(x) PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 3 Density Function ≥0 ∫ =1 < < =∫ Cutoff point level denoted by : > = f(x) a b PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 4 . Parameter Expected Value: = =∫ Variance: =∫ − =∫ − Standard Deviation = ( ) Cutoff point level , denoted by : > = PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 5 Example Example . Waiting time (hour), with density function 2 ∈ [0,1] = 0 ∉ [0,1] (a) Prob. of waiting more than a half of hour? (b) Prob. of waiting from 20 to 40 minutes? (c) The average and variance of waiting time? (d) Cutoff point level 10%? PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 6 Example . f(x) (a) > = ∫ 2 . / (b) < < = ∫/ 2 . f(x) (c) =∫ .2 . =∫ .2 . − 1/3 2/3 PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 7 . Uniform Distribution ~ ( , ) if ∈[ , ] = 0 ∉[ , ] a c d b = ; = < < = Ex. Temperature is Uniform Distribution in .