Question at position 8 Let X be a chi-squared random variable with degrees of freedom 14. What is P(X=14)?AnswerLet X be a chi-squared random variable with degrees of freedom 14. What is P(X=14)?[input]BlackTom题目解析

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Question at position 8 Let X be a chi-squared random variable with degrees of freedom 14. What is P(X=14)?AnswerLet X be a chi-squared random variable with degrees of freedom 14. What is P(X=14)?[input]BlackTom题目解析

BlackTom AI · Accepted Answer

The question asks for P(X = 14) where X ~ Chi-square with 14 degrees of freedom. In a continuous probability distribution like the chi-square, the probability of the random variable taking any exact single value is zero. Although the probability density function (pdf) f_X(x) at x = 14 is positive, the probability over a single point is the integral over an interval of width zero, which yields zero. Therefore, P(X = 14) = 0. A common misconception is to confuse the pdf value with an actual probability; remember that the pdf gives density, not probability, and probabilities are assigned to intervals, not points. The degrees of freedom (14) determine the shape of the distribution and the spread, but do not change the fact that a specific value has probability zero in a continuous distribution.

Question at position 8 Let X be a chi-squared random variable with degrees of freedom 14. What is P(X=14)?AnswerLet X be a chi-squared random variable with degrees of freedom 14. What is P(X=14)?[input]BlackTom题目解析

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