CHAPTER 12

Exercises

Exercise 1 (Section 2.1)

If

images

what is f−∞ p(x) dx ? Then what is imagesximages, imagesx2images, and imagesexp(x)images?

Exercise 2 (Section 2.1)

Show that the convolution of two Gaussian distributions,

images

is also a Gaussian.

Exercise 3 (Section 2.1)

Given the sets of random variables

imagesz1images = 0,

imagesz2images = 0,

varz1 = 1,

varz

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