Question

Let X be a continuous random variable with density function f(x)= |x|/10. What is the probability density function (PDF) for X?

A) f(x) = (x/10)
B) f(x) = (-x/10)
C) f(x) = (1/10)
D) f(x) = |x|/10

Answer 1

The given function f(x) = |x|/10 is the probability density function (PDF) for the continuous random variable X, as option D suggests. The graph of this distribution would show how the probability is distributed along the values of X, and the area under the curve is representative of the probability space, which totals to 1. The correct answer is option D

Step-by-step explanation:

Understanding the Probability Density Function (PDF)

The probability density function (PDF) of a continuous random variable is a function that describes the probability of the variable taking on a specific value within a continuous range. For example, the function given f(x) = |x|/10 is the PDF of the random variable X, suggesting that the probability is distributed along the values of X in proportion to the absolute value of X, scaled by 1/10.

To visualize this, we would draw a graph with the x-axis representing possible values of X and the y-axis representing the value of the PDF at each point X. The total area under the curve of this graph must be equal to 1 since the integral of the PDF over its entire range gives us the entire probability space, which is always 1 for a valid probability distribution. Note that for x outside the range where the PDF is defined, f(x) is zero.

For the continuous random variable X with a PDF of f(x) = |x|/10, option D (f(x) = |x|/10) is the correct representation of the PDF.