Homework SourseLet X be the number of rolls of a fair die before getting a
Let X be the number of rolls of a fair die before getting a 6, and let Y be the number of rolls before the first even number. Find E[X | y=5].
Solution
E(X/Y=5)=E(X/Y=5,X=5).P(X=5/Y=5)+E(X/Y=5,X>5).P(X>5/Y=5).
P(X=5/Y=5)=1/3
P(X>5/Y=5)=2/3
E(X/Y=5,X=5)=5
E(X/Y=5,X>5)=5+E(X)=5+6
E(X/Y=5)=1/3*5+2/3*(5+6)=9
![Let X be the number of rolls of a fair die before getting a 6, and let Y be the number of rolls before the first even number. Find E[X | y=5].Solution E(X/Y=5)=](/WebImages/19/let-x-be-the-number-of-rolls-of-a-fair-die-before-getting-a-1041146-1761540836-0.webp "Let X be the number of rolls of a fair die before getting a 6, and let Y be the number of rolls before the first even number. Find E[X | y=5].Solution E(X/Y=5)=")
