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[Step-by-Step] A random variable X is distributed uniformly between 9 and 21. Let f(x) and F (x) be the probability density function and cumulative distribution

Question: A random variable X is distributed uniformly between 9 and 21. Let f(x) and F (x) be the probability density function and cumulative distribution function for X, respectively.

  1. Find f(12), f (14), f(23), F(16), F(20), F(22).
  2. Suppose 25 realizations of X are taken independently and their sum is computed. Find the probability that the sum exceeds 400. Reminder: the variance of a random variable uniformly distributed between a and b is equal to

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