Q6. Which of the following is NOT an assumption of the binomial distribution?

A)   The trials are independent.

B)   Random variable X is discrete.

C)   The expected value is a whole number.

Q7. For a certain class of junk bonds, the probability of default in a given year is 0.2. Whether one bond defaults is independent of whether another bond defaults. For a portfolio of five of these junk bonds, what is the probability that zero or one bond of the five defaults in the year ahead?

A)  0.0819.

B)  0.4096.

C)  0.7373.

答案和详解如下：

Q6. Which of the following is NOT an assumption of the binomial distribution?

A)   The trials are independent.

B)   Random variable X is discrete.

C)   The expected value is a whole number.

Correct answer is C)         

The expected value is n × p. A simple example shows us that the expected value does not have to be a whole number: n = 5, p = 0.5, n × p = 2.5. The other conditions are necessary for the binomial distribution.

Q7. For a certain class of junk bonds, the probability of default in a given year is 0.2. Whether one bond defaults is independent of whether another bond defaults. For a portfolio of five of these junk bonds, what is the probability that zero or one bond of the five defaults in the year ahead?

A)  0.0819.

B)  0.4096.

C)  0.7373.

Correct answer is C)         

The outcome follows a binomial distribution where n = 5 and p = 0.2. In this case p(0) = 0.8⁵ = 0.3277 and p(1) = 5 × 0.8⁴ × 0.2 = 0.4096, so P(X=0 or X=1) = 0.3277 + 0.4096.

谢谢了 哈哈