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2 votes

The easy and the hard problems involving independent events

Suppose $X_1,\ldots,X_n$ are independent normally distributed random variables with expected value $\mu$ and variance $\sigma^2.$ Let $\overline X = \text{the sample mean} = (X_1+\cdots+X_n)/n$ and $S^...
Michael Hardy's user avatar
0 votes

Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

This is probably more of a psychological point than a mathematical one, but maybe it's easy to focus too much on the idea of having a range of values to choose from, and lose sight (at least ...
gidds's user avatar
  • 405
1 vote

Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

Did you consider the fact that your students have a point? When playing the lottery, let's say that the numbers $1$, $2$ and $3$ are popular, while $4$ is not. Being a popular number means that ...
Dominique's user avatar
  • 2,165
5 votes
Accepted

Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

I'd say (time permitting) put it to a practical test. Take a standard 6-sided die, say you're going to roll it 100 times. You (the instructor) guess "1" every time, while the student can ...
Daniel R. Collins's user avatar

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