Chapter 15, Problem 5RCC

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Let *f* be a joint density function of a pair of continuous random variables *X* and *Y.*

(a) Write a double integral for the probability that *X* lies between *a* and *b* and *Y* lies between *c* and *d.*

(h) What properties does *f* possess?

(c) What are the expected values of *X* and *Y*?

(a)

To determine

**To write:** The double integral for the probability that *X* lies between *a* and *b* and*Y* lies between *c* and *d*.

Explanation

**Given:**

The joint density function of a pair of continuous random variables *X* and *Y* is denoted by *f.*

The probability that *X* lies between *a* and *b* and *Y* lies between *c* and *d* is given by,

(b)

To determine

**To explain:** The properties of *f*.

(c)

To determine

**To explain:** The expected values of *X* and *Y.*

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