A, B, and C take turns flipping a coin. The first oneto get a head wins. The sample space of this experimentcan be defined byS =%1, 01, 001, 0001, . . . ,0000 (a) Interpret the sample space.(b) Define the following events in terms of S:(i) A wins = A.(ii) B wins = B.(iii) (A B)c.Assume that A flips first, then B, then C,then A, and so on.
X, Y Bivariate Random Variables f(u1, 2 ) is density of (X,Y) ∫ ( ) density of X ∫ ( ) density of Y X, Y are independent if f(u1, 2 = f1(u1 2 (u2) If X1, ,2…….X are nndependent Var(X 1 ……..X ) = n + …….. We want to produce to specification “m” “m” = length of a part, content of juice can etc We want to check at the end of the assembly line, if we are meeting the quality of the product (Quality-Control) Process: We choose a sample of size “n” from the product X 1 X 2 …….X n are independent random variables. They have the same distribution. Look at the average of the If X is a random variable then Var(aX) Var( ) = = = ( We
