Let X and Y be jointly continuous random variables with joint PDF,    , for     Find the value of the constant  that makes this a joint probability density function.

A cake factory produces on average 5 cakes per minute. Calculate the probability that 4 or more cakes will get produced in 2 minutes.

Mio, a restaurant owner, wants to test if her two managers perform at the same level. To do that, she collects data about the number of customer complaints at two random samples of shifts (one for each manager) Assume data is normally distributed and assume equal variances.   Here is a summary of the results:

A synthetic fiber has tensile strength is distributed with mean 76 psi and and standard deviation 4 psi. What is the probability that a random sample of eight specimens will have tensile strength that exceeds 78 psi?

A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random sample of 1423 adults from this city, the proportion that are vegetarian is 0.085.   Find a 90% confidence interval for the proportion of all adults in the city of Darby that are vegetarians.

Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 6 days. Let a random variable X denote the time (in days) until the next change.   What is the probability that the next change occurs in less than 4.5 days?

Which of the following is the formal charge by the House of Representatives that a government official has committed “treason, bribery, or other high crimes and misdemeanors”?

The _____ is the highest court in a particular state; this court primarily serves an appellate function.

If a president claimed that they possessed the authority to execute acts of Congress according to their own understanding of the law and the nation’s interests, they would be operating under the theory of

When President Obama prohibited federal agencies and contractors from discriminating against transgender employees, he made use of which of the following tools to do so?