Questions from Applied Statistics

Q: The probability density function of the time you arrive at a terminal

The probability density function of the time you arrive at a terminal (in minutes after 8:00 A.M.) is f (x) = 0.1 exp(−0.1x) for 0 < x. Determine the probability that a. You arrive by 9:00 A.M. b. You...

Q: The probability density function of the time it takes a hematology cell

The probability density function of the time it takes a hematology cell counter to complete a test on a blood sample is f (x) = 0.04 for 50 < x < 75 seconds. a. What percentage of tests requires more...

Q: The time it takes a cell to divide (called mitosis)

The time it takes a cell to divide (called mitosis) is normally distributed with an average time of 1 hour and a standard deviation of 5 minutes. a. What is the probability that a cell divides in less...

Q: The sick-leave time of employees in a firmin a month

The sick-leave time of employees in a firmin a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours. a. What is the probability that the sick-leave time for next...

Q: Show that the following function satisfies the properties of a joint probability

Show that the following function satisfies the properties of a joint probability mass function: Determine the following: a. P(X c. P(X 0.5, Y e. E(X), E(Y), V(X), V(Y) f. Marginal probability distrib...

Q: The percentage of people given an antirheumatoid medication who suffer severe,

The percentage of people given an antirheumatoid medication who suffer severe, moderate, or minor side effects are 10, 20, and 70%, respectively. Assume that people react independently and that 20 peo...

Q: Determine the value of c such that the function f (x

Determine the value of c such that the function f (x, y) = cx2y for 0 < x < 3 and 0 < y < 2 satisfies the properties of a joint probability density function. Determine the following: a. P(X < 1, Y < 1...

Q: A continuous random variable X has the following probability distribution:

A continuous random variable X has the following probability distribution: f (x) = 4xe−2x , x > 0 a. Find the moment-generating function for X. b. Find the mean and variance of X.

Q: The joint distribution of the continuous random variables X, Y,

The joint distribution of the continuous random variables X, Y, and Z is constant over the region x2 + y2 ≤ 1, 0 < z < 4. Determine the following: a. P(X2 + Y2 ≤ 0.5) b. P(X2 + Y2 ≤ 0.5, Z < 2) c. Jo...

Q: Contamination problems in semiconductormanufacturing can result in a functional defect, a

Contamination problems in semiconductormanufacturing can result in a functional defect, a minor defect, or no defect in the final product. Suppose that 20%, 50%, and 30% of the contamination problems...