aianjie

 

The sample size is:

A) 1.

B) 16.

C) 5.

D) 50.

aianjie

 

The correct answer is B

The sample size is the sum of all of the frequencies in the distribution, or 3 + 7 + 3 + 2 + 1 = 16.

aianjie

 

The relative frequency of the second class is:

A) 10.0%.

B) 0.0%.

C) 16.0%.

D) 43.8%.

aianjie

 

 

The correct answer is D

The relative frequency is found by dividing the frequency of the interval by the total number of frequencies:7/16=43.8%

aianjie

 

2、How is the relative frequency of an interval computed?

A) By dividing the sum of the two interval limits by 2.

B) By dividing the frequency of that interval by the sum of all frequencies.

C) By multiplying the frequency of the interval by 100.

D) By subtracting the lower limit of the interval by the upper limit.

aianjie

 

The correct answer is B

The relative frequency is the percentage of total observations falling within each interval. It is found by taking the frequency of the interval and dividing that number by the sum of all frequencies.

aianjie

 

AIM 4: Explain Bayes’ theorem and use Bayes’ formula to determine the probability of causes for a given event.

1、Bonds rated B have a 25% chance of default in five years. Bonds rated CCC have a 40% chance of default in five years. A portfolio consists of 30% B and 70% CCC-rated bonds. If a randomly selected bond defaults in a five-year period, what is the probability that it was a B-rated bond?

A) 0.625.

B) 0.429.

C) 0.211.

D) 0.250.

aianjie

 

The correct answer is C

According to Bayes' formula: P(B/default) = P(default and B)/P(default).

P(default and B )= P(default/B) × P(B) = 0.250 × 0.300 = 0.075

P(default and CCC) = P(default/CCC) × P(CCC) = 0.400 × 0.700 = 0.280

P(default) = P(default and B) + P(default and CCC) = 0.355

P(B/default) = P(default and B)/P(default) = 0.075 / 0.355 = 0.211

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2、The probability of A is 0.4. The probability of AC is 0.6. The probability of (B|A) is 0.5, and the probability of (B|AC) is 0.2. Using Bayes’ formula, what is the probability of (A|B)?

A) 0.875.

B) 0.125.

C) 0.375.

D) 0.625.

aianjie

 

The correct answer is D

Using the total probability rule, we can compute the P(B):

P(B) = [P(B|A) × P(A)] + [P(B|AC) × P(AC)]

P(B) = [0.5 × 0.4] + [0.2 × 0.6] = 0.32

Using Bayes’ formula, we can solve for P(A|B):

P(A|B) = [ P(B|A) / P(B) ] × P(A) = [0.5 / 0.32] × 0.4 = 0.625