Which of the following is true about independent random variables X and Y?

Study for the Society of Actuaries Exam P. Immerse in flashcards and multiple-choice questions, each with hints and explanations. Gear up for your exam success!

For independent random variables X and Y, the covariance between them is zero. This is a fundamental property of independent random variables. Covariance measures how much two random variables change together, and when two random variables are independent, the occurrence of one does not affect the occurrence of the other. Therefore, their joint variability can be expressed as the product of their individual variabilities, leading to a covariance of zero.

The other choices involve misinterpretations of the relationships or properties associated with independent random variables. For example, the first choice suggests that the covariance equals the sum of the variances, which is incorrect because covariance does not operate this way, particularly for independent variables. The third choice incorrectly relates covariance to the expected values, while the fourth choice mischaracterizes the variance of the product of two independent variables. For two independent random variables, the correct formula involves the variances in a different form, specifically that the variance of the product is not simply the product of the variances but involves additional computations. Hence, choice B accurately captures the essential property of independence regarding covariance.