Question

1. Daily production produces 50,000 balloons. It is known that theproduction process produces 0.004% defective balloons (i.e., the probability that a randomly selected balloon is defective is 0.00004). Whether one balloon is defective or not is independent of all other balloons. From one day’s production, estimate the chance of producing at least 3 defective balloons.

2.  A shipment contains 100 I-Pods, 8 of which are defective. I sample 4I-Pods from the shipment of 100 I-Pods at random. Estimate the chance of exactly one defective in my sample if I sample from the lot of 100 I-Pods:

(a) Without replacement:  (8 pts)

(b) With replacement:  (7 pts)

3. (10 points) Suppose that random variables X has pdf given by:

fX(x) = 3(1 – x2)/4, -1 ≤ x  ≤ 1.

(a) Show that the expected value (mean) of X, E[X] = μX = 0. (5 pts)

(b) Show that the variance of X is 1/5.  (5 pts)

Answer 1

m = 50,000 Þ= 0.0000 4 Solution - (1) PL atleast 3 defective) = 1-SP(x=0) + P(X= 1) + P(x=2} 1(50,000) (0.00004)(10.0000 4) 50000-X 00004) (1-0.0000 4) Xo = = 1 - 0.6768 0.3233 C ) Too I-Pods 92 Non def-echire (B) 8 defective (A) P (Exactly one defective) - 1913) - 1959 or 10.2562 (3) f(x)= 3(1-4), -15x5! Mean= E(x) = Sa tim da s'an. 3xdx 31-32

El palm de - Setnas de 3 11 variance = E(X). El variance -