Which of the following statements is a requirement for a function to be a probability density function?  Select all that apply.

If wealth increases, the demand for stocks ________ and that of long-term bonds ________, everything else held constant.

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The following table shows the joint distribution of X and Y. f(x, y) x y 2 4 1 0.12 0.08 3 0.30 0.20 5 0.18 0.12 (a) Find E(8X−4Y).  [blanka] (b) Compute P(Y ≤ 2 | X=4).  [blankc] For each part, enter your numeric answer as a decimal. Do not round.  

At a certain factory the thickness of a washer manufactured has mean = 12mm and variance = 0.5625mm. What is the largest probability that the washer thickness will be at the boundary or beyond the acceptance interval of 10.9 to 13.1? Hint: We are NOT ASSUMING NORMALITY and you will need to use a probabilistic inequality statement.  

Suppose that a researcher is interested in the average standardized test score for fifth graders in a local school district.  The group of fifth graders in the local school district is the [pop] and the average standardized test score across this group is the [parameter] of interest to the researcher. The fifth graders at a specific school would comprise a​ [sample] and their mean test score would be a​ [stat].

The purpose of the commitment by the Fed to keep the federal funds rate at zero for a long period of time is to

This table represents the probability distribution of a discrete random variable. Value of x 1 2 3 4 P(X = x) 0.3 -0.1 0.5 0.3  

The number of messages received at a computer bulletin board occurs with a mean rate of 6 messages per hour.  What is the probability that (strictly) fewer than 3 messages are received in 0.41 hour?    

Suppose there are ten​ five- and​ six-year-olds attending a birthday party. When a​ 30-year-old mother walks into the room with an infant in her​ arms, what happens to the mean age in the​ room? What happens to the standard deviation of ages in the​ room?