Final answer:
Without the underlying probability mass function (PMF) data, it is not possible to definitively validate the accuracy of the given cumulative distribution function (CDF) and the expected number and variance of defective items. The truth of the statement cannot be determined with the provided information alone.
Step-by-step explanation:
The student's question deals with the probability mass function (PMF) and the cumulative distribution function (CDF) of a discrete random variable X, which represents the number of defective items in a sample of 3. The statement claims that the CDF is a step function that rises at each of the points X=0, 1, 2, and 3 with probabilities 0.477, 0.973, 0.995, and 1, respectively. Additionally, it asserts that the expected number of defective items (mean) E(X) is 0.733 and the variance of X is 0.489. To evaluate the statement's truth, one would need to analyze the probabilities provided and calculate the expected value and the variance of X to confirm whether they are indeed 0.733 and 0.489, respectively.
However, we are not provided with the probability mass function required to verify these calculations, nor can we accept the given probabilities for the CDF without seeing the PMF. If we assume that the given CDF and the expected value and variance are derived correctly from the corresponding PMF, then the provided statement could be true. Yet, without this underlying PMF data, we cannot definitively state the accuracy of the given information. Therefore, the answer to the question is not conclusively true or false based on the information provided.
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