5.28.2005

Q&A: What is the probability that the penalty paid is...

...greater than 7% and less than 12%, assuming that the penalty for withdrawing funds early from a certain account follows a uniform distribution on the interval from (5%, 10%).

A

  • Because the density ends at 10, there is no probability associated with X values greater than 10. So P(7 < X < 12) is the same as P(7 < X < 10)
  • F(10)-F(7) = 1-F(7) = 1 - (x - a)/(b - a) = 1 - (7-5)/(10-5) = 0.6

Bonus Points

  • aka a rectangular distribution. can be discrete or continuous.
  • For a continuous uniform random variable,
    • The probability density function is: f(x) = 1 / (b - a) for a <= x <= b; or 0 otherwise.
    • The cumulative density function is: F(x) = 0 for x <= a; (x - a)/(b - a) for a <= x <= b; 1 for x >= b.
    • the distribution is symmetric: the mean = median.
    • the mean = (a + b)/2, and the variance = (b - a)^2/12.

Category: C++ Quant > Quantitative Analysis > Probability > Distribution

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