Asked by
Destiny Cooper
on Nov 27, 2024
Verified
The normal random variable's density function is (1) single-peaked above the variable's mean, median, and mode, all of which are equal to one another, (2) perfectly symmetric about this peaked central value and, thus, bell-shaped, and (3) characterized by tails extending indefinitely in both directions from the center, approaching (but never touching) the horizontal axis, which implies a positive probability for finding values of the random variable anywhere between minus infinity and plus infinity.
Density Function
A mathematical function that describes the probability distribution of a continuous random variable, indicating how the total probability is distributed over the various possible values the variable can take.
Symmetric
A characteristic of shapes, equations, or other entities that remain unchanged when reflected, rotated, or transformed in specific ways.
Tails
The ends of a distribution curve, referring to the extreme values far from the mean in a probability distribution.
- Understand the basic properties and characteristics of the normal distribution.
- Understand the relationship between probabilities and areas under the normal curve.
Verified Answer
JL
Learning Objectives
- Understand the basic properties and characteristics of the normal distribution.
- Understand the relationship between probabilities and areas under the normal curve.