Question

Suppose that the weight of a certain breed of small dog can range up to 10 pounds. Let (f_w) denote the PDF of the dog weight, where (f_w(x)).

a) (f_w(x) = 0)
b) (f_w(x) = 1)
c) (0 ≤ f_w(x) ≤ 1)
d) (f_w(x) > 1)

Answer 1

The correct answer is (c) because the Probability Distribution Function (PDF) for a given weight x of a small dog should satisfy the condition 0 ≤ fw(x) ≤ 1, meaning the PDF at any point should be between zero and one inclusive.

Step-by-step explanation:

The question pertains to the concept of a Probability Distribution Function (PDF) for weights of a certain breed of small dog. Since weights are continuous values, we expect the PDF, fw(x), to satisfy certain properties. Specifically, the value of the PDF at any given point x, where x is a possible value of weight (within the range of 0 to 10 pounds for small dogs), should satisfy the condition that 0 ≤ fw(x) ≤ 1. This means that option (c) is correct, because PDF values represent the density of probability at a point and must be between 0 and 1 inclusive. Options (a), (b), and (d) are incorrect for a PDF since the PDF cannot be exactly 0 or 1 for all x, and cannot be greater than 1. Furthermore, for a discrete random variable, the probabilities assigned to each value of x must sum up to 1, as noted in the reference information provided.