Questions from Applied Statistics

Q: An article in Mathematical Biosciences [“Influence of Delayed Viral Production on

An article in Mathematical Biosciences [“Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients” (1998, Vol. 152(2), pp. 143–163)] considered the time delay between the ini...

Q: Derive the probability density function for a lognormal random variable Y from

Derive the probability density function for a lognormal random variable Y from the relationship that Y = exp(W) for a normal random variable W with mean θ and variance ω2.

Q: Powermeters enable cyclists to obtain power measurements nearly continuously. The meters

Powermeters enable cyclists to obtain power measurements nearly continuously. The meters also calculate the average power generated over a time interval. Professional riders can generate 6.6 watts per...

Q: According to results from the analysis of chocolate bars in Chapter 3

According to results from the analysis of chocolate bars in Chapter 3, the mean number of insect fragments was 14.4 in 225 grams. Assume that the number of fragments follows a Poisson distribution. a....

Q: The time between arrivals of small aircraft at a county airport is

The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. a. What is the probability that more than three aircraft arrive within an hour? b....

Q: The time between calls to a corporate office is exponentially distributed with

The time between calls to a corporate office is exponentially distributed with a mean of 10 minutes. a. What is the probability that there are more than three calls in one-half hour? b. What is the pr...

Q: Derive the formula for the mean and variance of an exponential random

Derive the formula for the mean and variance of an exponential random variable.

Q: If the random variable X has an exponential distribution with mean θ

If the random variable X has an exponential distribution with mean θ, determine the following: a. P(X > θ) b. P(X > 2θ) c. P(X > 3θ) d. How do the results depend on θ?

Q: Suppose that x has a beta distribution with parameters α = 2

Suppose that x has a beta distribution with parameters α = 2.5 and β = 1. Determine the following: a. P(X < 0.25) b. P(0.25 < X < 0.75) c. Mean and variance

Q: Suppose that X has a beta distribution with parameters α = 2

Suppose that X has a beta distribution with parameters α = 2.5 and β = 2.5. Sketch an approximate graph of the probability density function. Is the density symmetric?