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gremar0976
22.02.2021 •
Mathematics
An integrated circuit factory has three machines X, Y, and Z. Test one integrated circuit produced by each machine. Either a circuit is acceptable (a) or it fails (f). An observation is a sequence of three test results corresponding to the circuits for machines X, Y, and Z, respectively. For example, aaf is the observation that the circuits from X and Y pass the test and the circuit from Z fails the test.
a. What are the elements of the sample space of this experiment?
b. What are the elements of the sets:
ZF={circuit from Z fails},
XA ={circuit from X is acceptable}.
c. Are ZF and XA mutually exclusive?
d. Are ZF and XA collectively exhaustive?
e. What are the elements of the sets C={more than one circuit acceptable}, D={at least two circuits fail}.
f. Are C and D mutually exclusive?
g. Are C and D collectively exhaustive?
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Ответ:
Kindly check explanation
Step-by-step explanation:
Acceptable = a
Fails = f
For machines X, Y, Z ;
Sample space, S = {aaa, aaf, aff, fff, faa, afa, ffa, faf}
Total elements in sample space = 8
B.)
Elements of the set:
ZF={circuit from Z fails},
XA ={circuit from X is acceptable}.
ZF = {aaf, aff, fff, faf}
XA = {aaa, aaf, aff, afa}
C.)
c. Are ZF and XA mutually exclusive?
Check if ZF n XA = ∅
ZF n XA = {aaf, aff}
Hence, ZF and XA are not mutually exclusive
d. Are ZF and XA collectively exhaustive?
To be collectively exhaustive :
ZF u XA = Sample space
ZF u XA = {aaa, aaf, aff, afa, faf, fff}
{aaa, aaf, aff, afa, faf, fff} ≠ sample space
Hence, ZF and ZA are not collectively exhaustive.
e. What are the elements of the sets
C={more than one circuit acceptable},
C = {aaa, aaf, faa, afa}
D={at least two circuits fail}.
D = {ffa, faf, aff, fff}
f. Are C and D mutually exclusive?
Check if C n D = ∅
C n D = ∅
Hence, A and D are mutually exclusive
g. Are C and D collectively exhaustive?
To be collectively exhaustive :
C u D = Sample space
C u D = {aaa, aaf, aff, afa, faf, fff}
{aaa, aaf, faa, ffa, aff, afa, faf, fff} = sample space
Hence, C and D are collectively exhaustive.
Ответ:
To round to the nearest thousand, take apart the number so that you only have x thousand.
4,392
Now, take the second highest number (hundred) and if it is 1-4 then it stays the same. If it's 5+, then it would go up one. In this case, since the hundreds place is 3, the number would stay the same.