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: Graph A, C, D and E.

How to determine the density curves?

In Geometry, the area of the density curves for a continuous random variable must always be equal to one (1). Thus, we would test this rule in each of the curves:

Area A = (1 × 5 + 1 × 3 + 1 × 2) × 0.1

Area A = 10 × 0.1

Area A = 1 sq. units (True).

For curve B, we have:

Area B = (3 × 3) × 0.1

Area B = 9 × 0.1

Area B = 0.9 sq. units (False).

For curve C, we have:

Area C = (3 × 4 - 2 × 1) × 0.1

Area C = 10 × 0.1

Area C = 1 sq. units (False).

For curve D, we have:

Area D = (1 × 4 + 1 × 3 + 1 × 2 + 1 × 1) × 0.1

Area D = 10 × 0.1

Area D = 1 sq. units (True).

For curve E, we have:

Area E = (1/2 × 4 × 5) × 0.1

Area E = 10 × 0.1

Area E = 1 sq. units (True).

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