106k views
4 votes
The management of XYZFinity Cable estimates that the number of new subscribers (in thousands) next to Charlottesville is described by the random variable X, and the number of new subscribers (in thousands) in Albemarle County outside Charlottesville is described by the random variable Y. If the joint probability density function is given by:

f(x, y) = xy(4-y)(25-x²)/4000

on the domain {0 <= x <= 5; 0 <= y <= 4}, find the probability that the number of new subscribers in Charlottesville will be between 4000 and 5000, and the number of new subscribers in Albemarle County will be between 1000 and 2000.

User Bardt
by
7.7k points

1 Answer

5 votes

Final answer:

The random variable X in the question represents the number of new XYZFinity Cable subscribers in Charlottesville (in thousands). The probabilities concerning renting DVDs cannot be calculated as the specific probability distribution needed for these calculations is not available in this context.

Step-by-step explanation:

Describing the Random Variable X and Computing Probabilities

The random variable X described in the original question refers to the number of new subscribers (in thousands) for the XYZFinity Cable in Charlottesville within the given domain. To address the other parts of the student's inquiry related to different questions,

Random variable X generally represents a specific measurement or category determined by the context of the situation, such as the number of subscribers in this case.

To find the probability of a customer renting three DVDs, we would need the probability distribution function relevant to DVD rentals which is not provided in this context.

The same is true for finding the probability of a customer renting at least four DVDs or at most two DVDs; without the specific probability distribution, this cannot be answered here.

Without the proper context and associated probability distributions for the DVD rental scenarios, it's not possible to calculate the probabilities mentioned. The student might be referring to different parts of their study material which would need to be consulted in order to find the appropriate probabilities.

User Caleb Seadon
by
8.4k points