Question

The following graphs have a scale assigned to them: The area of each grid square is 0.1 sq. units. Which ones are density curves for a continuous random variable? Check all that apply. A. Graph A B. Graph B C. Graph C D. Graph D E. Graph E

Answer 1

The graphs that are density curves for a continuous random variable are

A. Graph A

C. Graph C

D. Graph D

E. Graph E

How to determine the density curves

To find the density curves for a continuous random variable, we would have the following calculations for the area;

1. Area A = (1 * 5) + (1 * 3) + (1 * 2) * 0.1

= 10 * 0.1

= 1

2. Area B = (3 * 3) * 0.1

= 9 * 0.1

0.9 ≠ 1

3. (3 * 4) - (2 * 1) * 0.1

= 10 * 0.1

= 1

4. Area D = (1 * 4 + 1 * 3 + 1 * 2 + 1 * 1) * 0.1

= 10 * 0.1

= 1

5. Area E = (1/2 * 4 * 5) * 0.1

= 10 * 0.1

= 1

So, all the areas that equate to 1 form density curves for a continuous random variable.