The probability density function of X, the lifetimeof a certain type of electronic device (measured inhours), is given by (a) Find P{X > 20}.(b) What is the cumulative distribution functionof X?(c) What is the probability that, of 6 such types ofdevices, at least 3 will function for at least 15hours? What assumptions are you making?
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
