STAT 305B Fall 2007
Homework 5–Due 9/27
•Reading Assignment: A.1.3 on independence. Ch 5:5.1.1-5.1.3
•Problem 1: Widgets produced in a factory can be classified as defective, marginal or good. At
present, a machine is producing about 5% defective, 15% marginal and 80% good widgets. An
engineer plans the following method of checking on the machine’s adjustment: Two widgets will
be sampled initially, and if both are defective, the machine will be immediately adjusted. If both
are good, testing will cease without adjustment. If neither of these first two possibilities occurs, an
additional three widgets will be sampled. If all three of these are good, or two are good and one is
marginal, test will cease without machine adjustment. Otherwise, the machine will be adjusted.
(a) Evaluate P(only two widgets are sampled).
(b) Evaluate P(no adjustment is made).
(c) Are the events (only two widgets are sampled) and (no adjustment is made) independent
events? Explain.
•Problem 2: P331-39.
•Problem 3: Discrete random variables can be defined on infinitely many isolated/separated values.
Let Xbe a random variable whose sample space being the natural numbers N={1,2,...}and let
f(x) = 1
2x,
i.e. P(X= 1) = f(1) = 1/21,P(X= 2) = f(2) = 1/22,. . . .
Verify that Xis a properly defined discrete random variable, i.e (i) f(x)>0 for any x∈Nand
(ii) Px∈Nf(x) = 1.
1