05. PDF of the normal distribution

PRDTM2-787 AI Trading C4 L1 Vid5 The PDF Of The Normal Distribution

Understanding the Normal Distribution and Probability

Grasping the concepts of mean and standard deviation paves the way to comprehending the normal distribution:

  • Mean and Standard Deviation: These are essential parameters defining a normal distribution. Using these, everything about a distribution can be calculated.
  • Example: Human IQ is normally distributed, with a mean of 100 and a standard deviation of 15.

Key Concepts

  • Probability Density Function (PDF): Parameterized by the mean ((\mu)) and standard deviation ((\sigma)), represented by the Greek letter (\phi).
  • Probability Calculations:
    • To compare IQ scores, such as if one individual's IQ exceeds another's, the integral of the PDF is calculated from a specified IQ score to infinity.

Real-World Application

  • John's IQ of 120: The probability of encountering someone with a higher IQ is about 9.1%.
  • Einstein Example: The likelihood of finding someone with an IQ above 175, presumed to be Einstein’s, is extremely rare (2.87 in 10 million). This illustrates the steep decline in probabilities for higher IQs within a population.

What is the PDF of a normal distribution?
SOLUTION: The probability density function of the normal distribution.

"The PDF of a normal distribution is always positive." - Is this correct?
SOLUTION: yes

Where does the PDF of a normal distribution have its maximum value?
SOLUTION: the mean of the distribution

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