18.44 Lecture Notes - Lecture 8: Random Variable, Gambling, Fair Coin
Document Summary
A random variable x is a function from the state space to the real numbers. We can interpret x as a quantity whose value depends on the outcome of an experiment. Example: toss n coins and let x be the number of heads. The state space consists of the set of all 2 possible coin sequences. In n coin toss example, knowing the values of some coin tosses tells us nothing about the others. Say e e are independent if for each {i , i , , i } {1, 2, , n} we have p(e e e ) = p(e )p(e )p(e ) Independence implies p(e e e |e e e ) = p(e e e ) = Shuf e n cards, and let x be the position of the jth card. The state space consists of all n! possible orderings. We get that p{x = k} = 1/n.
