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Q: Is probability density function and gaussian distribution function are same?

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probability density distribution

Assuming that you are considering a N(0,1) Gaussian distribution, the answer is approximately 1 in 20. The 0.95%ile (two tailed) occurs at -1.96 and 1.96.

A probability density function (pdf) for a continuous random variable (RV), is a function that describes the probability that the RV random variable will fall within a range of values. The probability of the RV falling between two values is the integral of the relevant PDF. The normal or Gaussian distribution is one of the most common distributions in probability theory. Whatever the underlying distribution of a RV, the average of a set of independent observations for that RV will by approximately Gaussian.

A probability density function assigns a probability value for each point in the domain of the random variable. The probability distribution assigns the same probability to subsets of that domain.

A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.

The Gaussian probability density distribution (pdf) is referred to as the Normal distribution. The Gaussian model results in a Gaussian pdf. Interesting, it didn't come from Gauss, but de Moivre, one of the greatest mathematicians of the 18th century, at least in my opinion. See related links.

A probability density function.

That's a Gaussian distribution.

what is density curve

Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.

A probability density function.

Normal distribution is the continuous probability distribution defined by the probability density function. While the binomial distribution is discrete.

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