5.31.2005

Q&A: What's the probability of a normal random variable X...

...equal to a particular value, say 15? what about P(X<mean)?

A:

  • P(X=15) = 0. Can only calculate the probability of x when it falls in a range, such as 14 < x < 16.56 > x > 54.
  • P(X<=mean) = P(X>=mean) = 50%. therefore P(X<mean) < 50%. The total area under the bell-shaped curve is 1.

Bonus Points

  • The normal distribution is completely described by two parameters: the mean (m) and the standard deviation (s).
  • For normal distributions with the same mean but difference variances: The higher the standard deviation the more speard out the distribution.
  • For normal distributions with the same variance but difference means: the mean locates the axis of symmetry.
  • The normal distribution is symmetric: mean = median = mode. it has a skewness of 0, a kurtosis (it measures the peakedness of a distribution) of 3, an excess kurtosis (which equals kurtosis less 3) of 0.
  • A linear combination of two or more normal random variables is also normally distributed.

Category: Quantitative Analysis > Probability > Distribution

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