This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 ACTL1001 Games of Chance (2) Outline: 1. Independence 2. Distributions in Actuarial Science (ctd) 3. Probability of Ruin 4. Simulation Reading (Req) Sherris, 2.32.7 2 Independence & Trials or events are independent if the occurrence of one does not the affect the probability of occurrence of any of the others. & The probability that a number of independent events occur is just the product of the probabilities that each event occurs. 3 Geometric & The Geometric distribution gives the probability of the number of trials to the first success where the probability of success on any trial is p . & Geometric ( p ) Pr ( X = x ) = (1 ¡ p ) x ¡ 1 p x = 1 ; 2 ::: E [ X ] = 1 p V ar [ X ] = 1 p & 1 p ¡ 1 ¡ 4 Example & Passing or gaining exemption from actuarial professional examinations is notoriously difficult. & Assume that the probability of passing or gaining an exemption from a particular actuarial professional examination is : 6 , and that the chance per attempt is the same and are independent. & Calculate the probability that it will take at least 3 attempts to pass or gain an exemp tion from this examination. 5 Exponential & The exponential distribution is used for the probability distribution of the time until an event occurs where the probability does not depend on elapsed time & Exponential distribution often used to model the time of survival Exponential ( & ) f ( x ) = e ¡ x & & x ¢ and otherwise F ( x ) = Z x ¡1 f ( t ) dt = 1 ¡ e ¡ x & x ¢ E [ X ] = & V ar [ X ] = & 2 6 Normal Distribution & The normal distribution is the “bell” shaped symmetric distribution that typically re...
View
Full Document
 One '09
 Nicole
 Actuarial Science, Normal Distribution, Variance, Probability theory, probability density function, Cumulative distribution function

Click to edit the document details