Consider a random variable X that follows a continuous uniform distribution: 7 <= X <=20. Which of the following statements is least accurate? A) F(10) = 0.23. B) F(21) = 0.00. C) F(12 <= X <= 16) = 0.307. D) F(6) = 0. The correct answer was B) F(21) = 0.00. F(21) = 1.00 The probability density function for a continuous uniform distribution is calculated as follows: F(X) = (X - a) / (b - a), where a and b are the upper and lower endpoints, respectively. (If the given X is greater than the upper limit, the probability is 1.0.) Shortcut: If you know the properties of this function, you do not need to do any calculations to check the other choices. The other choices are true. F(10) = (10 - 7) / (20 - 7) = 3 / 13 = 0.23 F(12 <= X <= 16) = F(16) - F(12) = [(16 - 7) / (20 - 7)] = 0.307 F(6) = 0 (if the given X is less than the lower limit, the probability is 0) ********************************************************************** Isnt the probability of X outside the boundaries zero? And if I believe that B is right than by same account D should be right too because it is between 7 ¡Ü X ¡Ü 20…
You’re mixing the concept of the cumulative distribution function and the density function. The value of the cumulative distribution function F at the point x measures the probability that X is less than or equal to x. Thus, F(21) = 1 since X is, with probability one, less than 21 as it is constrained to be in the interval [7,20]. Therefore statement B is not correct. However, statement D is correct because the probability that X is less than or equal to 6 is zero.