About Normal Distribution Formula
In probability and statistics, the normal distribution, often known as the bell curve or gaussian distribution, is the most important continuous probability distribution. A large number of random variables of importance in physical research and economics are either nearly or exactly characterised by the normal distribution. Other probability distributions can be approximated using the normal distribution formula.
Random variables with a normal distribution have values that can take on any known value within a certain range.
The probability density function f(x) for the continuous random variable X in the system defines the normal distribution. It's a function whose integral over an interval (say, x to x + dx) indicates the probability of the random variable X when the values between x and x + dx are taken into account. Because there are infinite values between x and x + dx, a range of x is taken into account, and a continuous probability density function is defined as
f(x)≥0 ∀ x∈(−∞,+∞)
∫+∞−∞f(x)=1
Normal distribution of a random variable X with mean = μ & variance = σ2, the probability density f(x) is given by :
An equivalent representation:
X∼N(π,σ2)
specific μ = 3 and a σ ranging from 1 - 3, the probability density function (p.d.f.) is as:
The probability density function of normal or a gaussian distribution is
- Where,
- x - variable
- μ - mean
- σ - standard deviation
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