習(xí)題:
  Exercise:
  Which of the following statements about the F-distribution and chi-squared distribution is least accurate? Both distributions:
  A    Are asymmetrical
  B    Are bound by zero on the left.
  C    Are defined by degree of freedom.
  D    As degrees of freedom decrease, both distributions converge to a normal distribution.
  解析:
  Answer: D
  Explanation: As degrees of freedom increase, both distributions converge to a normal distribution.
  知識(shí)點(diǎn):
  Chi-Squared Distribution and F-distribution
  Chi-Squared Distribution
  If we have k independent standard normal variables, Z1, Z2, …, Zk, then the sum of their squares, S, has a chi-squared distribution. The variable k is commonly referred to as the degrees of freedom.
  Properties:
  l  Because the chi-squared variable is the sum of squared values, it can only take on nonnegative values and is asymmetrical.
  l  The mean of the distribution is k, and the variance is 2k.
  l  As k approaches infinity, the chi-squared distribution converges to the normal distribution.
  F-distribution
  If U1 and U2 are two independent chi-squared distributions with k1 and k2 degrees of freedom, respectively, then X:
  follows an F-distribution with parameters K1 and K2.
  Because the chi-squared PDF is zero for negative values, the F-distribution’s density function is also zero for negative values.
  As k1 and k2 approach infinity, the F-distribution converges to a normal distribution.
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