Question

3. A manufacturer of semiconductor devices takes a random sample of 100 chips and tests them, classifying each chip as defective or nondefective. Let X; = 0 if the chip is nondefective and Xi = 1 if the chip is defective. The sample fraction defective is X1 + X2 + ... + X100 100 What is the sampling distribution of the random variable ?

Answer 1

lucky Page No: Date : Xi - SI if chip is de fective to if chip is non-defective. P. Xi v Bernoulli disto with parameter p is probability of success ie probability of chip being defective. Now, = Xit Xzt. + X 100 100 7 T = np = Xit Xat ---+ X 100 T is sum of loo independent bernoulli random variables: T= 100x po Binomial (n=100; p As sample size is large, (100). T- ECT) NcOid). VCT)

Lucky Page No.: Date : I T= np= loop ЕСт) = np= 100 p V (T) np (1-P) - 100p (1-0) I 100 p - loop too piip N ACOLL) -P w Need P(1-P TOO 11 . N ( e. P, P (1-P) 100 For large n Cice. 100) EC) = pe vep) - P(1-P) NN (ECP) =p 100