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What does the mean have to do with a normal distribution?
Almost all statistical distribution have a mean. It is the expected value of the random variable which is distributed according to that function.
The expected value is what kind of aspect of how probability distribution is characterized?
Expected value is the outcome of confidence of how probability distribution is characterized. If the expected value is greater than the confidence interval then the results are significant.
What is the different between standard normal distribution and normal distribution?
A normal distribution can have any value for its mean and any positive value for its variance. A standard normal distribution has mean 0 and variance 1.
Can the expected value of a discrete probability distribution be negative?
Yes it can be negative.
What is it meant by the expected value is observable?
The expected value is the arithmetic mean. It may not always be a value that is realised. Consider rolling a fair normal die. The mean or expected value of the outcome is 3.5 but a normal die will never ever turn up 3.5 since it has only integer values.
