Questions from Engineering Statistics

Q: For the random variables X and Y whose joint density function is

For the random variables X and Y whose joint density function is given in Exercise 3.40 on page 105, find the covariance.

Q: Given a random variable X, with standard deviation σX, and

Given a random variable X, with standard deviation σX, and a random variable Y = a + bX, show that if b < 0, the correlation coefficient ρXY = −1, and if b > 0, ρXY = 1.

Q: Consider the situation in Exercise 4.32 on page 119.

Consider the situation in Exercise 4.32 on page 119. The distribution of the number of imperfections per 10 meters of synthetic failure is given by Find the variance and standard deviation of the nu...

Q: In a gambling game, a woman is paid $3 if

In a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. If she draws any other card, she loses. How much s...

Q: For a laboratory assignment, if the equipment is working, the

For a laboratory assignment, if the equipment is working, the density function of the observed outcome X is Find the variance and standard deviation of X.

Q: For the random variables X and Y in Exercise 3.39

For the random variables X and Y in Exercise 3.39 on page 105, determine the correlation coefficient between X and Y . Exercise 3.39: From a sack of fruit containing 3 oranges, 2 apples, and 3 banana...

Q: Random variables X and Y follow a joint distribution /

Random variables X and Y follow a joint distribution Determine the correlation coefficient between X and Y .

Q: Referring to Exercise 4.35 on page 127, find the

Referring to Exercise 4.35 on page 127, find the mean and variance of the discrete random variable Z = 3X − 2, when X represents the number of errors per 100 lines of code. Exercise...

Q: An annexation suit against a county subdivision of 1200 residences is being

An annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. If the occupants of half the residences object to being annexed, what is the probability t...

Q: Using Theorem 4.5 and Corollary 4.6, find

Using Theorem 4.5 and Corollary 4.6, find the mean and variance of the random variable Z = 5X + 3, where X has the probability distribution of Exercise 4.36 on page 127. Exercise 4.36: Suppose that t...