MHB How can self-studying be an effective alternative to college education?

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Self-studying can be an effective alternative to college education for individuals who are self-motivated and disciplined. It allows for personalized learning at one's own pace, focusing on specific interests or career goals. However, it may not provide the same networking opportunities or structured environment that traditional college offers. The effectiveness of self-study largely depends on the individual's learning style and commitment. While it can work for some, it may not be suitable for everyone.
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-Dan
 
I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...

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