A discrete variable X can take on integer values of 1 to 10. A sample of size 50 results in the following probability estimates:
(a) Write out and graph the cumulative distribution.
(b) Calculate the following probabilities using the cumulative distribution: (1) X is between 6 and 10, and (2) X takes the value 4, 5, or 6.
(c) Use the cumulative distribution to show that P(X = 7 or 8) = 0.0. Even though this probability is zero, the statement about X is that it can take on integer values of 1 to 10. How do you explain the apparent contradiction in these two statements?
(c) P(X = 7 or 8) = F(8) – F(6) = 0.7 – 0.7 = 0.0
No sample values in the 50 have X = 7 or 8. A larger sample is needed to observe all values of X.
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