Probability Density Function (PDF) of Normal Distribution
The Probability Density Function (PDF) of a normal distribution, often denoted as f(x), describes the likelihood of a random variable taking on a specific value within the distribution. In simpler terms, it tells the probability of getting a particular result. For a normal distribution, the PDF is represented by the well-known bell-shaped curve. This curve is centered at the mean (average) value, and its shape is determined by the standard deviation, which measures how spread out the data is. The PDF shows that values near the mean are more probable, while values farther from the mean are less likely.
The PDF of a normal distribution is defined by:
, -∞ < x < ∞
Where,
- f(x) represents the probability density at a specific value x.
- μ is the mean, which indicates the center or average value of the distribution.
- σ is the standard deviation, which measures how spread out the data is.
- π is approximately 3.1416, a mathematical constant.
- e is the mathematical constant, measured at approximately 2.7183.
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