A bond quotes a rate of return of 9% and will pay $1,000 in one year with a probability of 69% and $0 with a probability of 31%.

What is the time premium?

What is the default premium?

In a certain country, the true probability of a baby being a boy is 0.517, Among the next nine randomly selected births in the country, what is the probability that one of them is a girl?

Use Excel to generate the probability distribution for a binomial random variable for which there are 20 trials (n = 20) and the probability of success is 0.5 (p = 0.5), and show the graph.

Given the cumulative distribution of an exponential random variable find:

1. The probability density function
2. Show that it is a valid probability function
3. The moment generating function
4. The Expected mean
5. The variance

1. What is the probability density function?

2. In the Business context, can anyone use an example to show how the probability density function is applied in the real world?

Given the cumulative distribution of a gamma random variable find:

1. The probability density function
2. Show that it is a valid probability function
3. The moment generating function
4. The Expected mean
5. The variance

A random sample of n=64 observations is drawn from a population with a mean equal to 51 and a standard deviation equal to 32.

a. Find the probability that overbar x is less than 43.

b. Find the probability that overbar x is greater than 57.

c. Find the probability that x over bar x falls between 43 and 59.

​(Round to three decimal places as​ needed.)

A typist makes an error while typing a letter 0.9% of the time. There are two types of errors. Type A and B
errors occur 30% and 70% of the time, respectively, whenever an error occurs.
(a) What is the probability of no error in 15 letters?
(b) What is the probability of no type A error in 15 letters?
c) given that exactly one error has occurred in 15 letters, what is the probability that it is a type A error?