Minimum of Normal Distribution Function

In summary, the minimum of normal distribution function is the lowest point on the curve of a normal distribution graph and is calculated using the formula μ - 3σ. It represents the lower limit of the expected range of values for a normally distributed variable and can be negative if the mean is negative and the standard deviation is relatively small. This function is used in statistical analysis to calculate probability, identify outliers, and determine expected ranges of values in a population.
  • #1
Painguy
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Homework Statement



Show that there is no minimum for the normal distribution function e^(-(x-μ)^2/(2 σ^2))/(sqrt(2 π) σ)

Homework Equations





The Attempt at a Solution



I figured I'd take the derivative and set it equal to 0, but then what?
 
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  • #2
Painguy said:
I figured I'd take the derivative and set it equal to 0, but then what?
What is the answer you got? And then, how do you tell the difference between a maximum and a minimum?
 

Related to Minimum of Normal Distribution Function

1. What is a minimum of normal distribution function?

A minimum of normal distribution function refers to the lowest point on the curve of a normal distribution graph. It represents the smallest value that a variable can take in a normally distributed dataset.

2. How is the minimum of normal distribution function calculated?

The minimum of normal distribution function is calculated using the formula μ - 3σ, where μ is the mean and σ is the standard deviation of the dataset. This formula assumes that the dataset is normally distributed.

3. What does the minimum of normal distribution function signify?

The minimum of normal distribution function signifies the lower limit of the expected range of values for a normally distributed variable. It is also known as the lower bound, and any values below this minimum are considered outliers.

4. Can the minimum of normal distribution function be negative?

Yes, the minimum of normal distribution function can be negative if the mean (μ) is negative and the standard deviation (σ) is relatively small. This indicates that there is a high probability of getting values that are lower than the mean in a normally distributed dataset.

5. How is the minimum of normal distribution function used in statistical analysis?

The minimum of normal distribution function is used to calculate the probability of a value being within a specific range in a normally distributed dataset. It is also used to identify outliers and determine the expected range of values for a variable in a population.

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