Question

10. Multiple Choice Question It is known that a particular company produces products of which 30% are defective. We select items at random and identify it as being defective or not. Calculate the probability that the sixth selected item will be the 3rd defective. A. 0.38282 B. 0.09261 C. 0.24518 D. 0.75494 E. none of the above 11. Multiple Choice Question Let X1,..., X10 be a random sample from a population with mean y and variance o?. Consider the following estimators for je: X: +.. ... + X10 3X1 - 2X: +3X10 10 2 Are these estimators unbiased (i.e. is their expectation equal to p)? A. Both estimators are unbiased. C. Only the second is unbiased. E. Insufficient information. B. Both estimators are biased. D. Only the first is unbiased.

Answer 1

10) Let x = Number of defective XN B(n = 6 p= 0 30) pm. f of x given as then h-x P(x=x) = "cæ p (.pt ; 80,1,2,., OLPE 7 for a given information p.mer become PlX=8) ocze (0:30) (1-0:30) He=0.1.2 t-x 6 OLO 30L -N the probability that 3rd we have to find defective 15 P(X= 3) 6-3 p(x=3) = GC3 (0:30) 3 (1-0.30) GO 0.18 522 option E) is correct E) none of the above (1) Here X X2 xn be a random sample from a with mean M and variance population 62 Now E(X)= E(X2) = E(X) = M As we know somple mean is unbiased estimator of population mean iff E(X)= u CS Scanned with CamScannen

시 have given that estimators for ê = X1 + X2+...+ X10 Now consider ECô) = X10) Xitxat....t lo E(X) + F(X2) + F(X3) +...+ E(Xio) l + Mt et kthAM + + M + H+ lou = 시 i is unbiased estimator of u 3x, -285 +3810 2 E cê, ) = 3E(xi) - 2 ECX5) + 3 E(X10) 3 M-2 M +34 2 11 44 2 ECô) 24 ô2 is not unbiased estimator of el D) option is correct D) or only the first is unbiased CS Scanned with CamScanner