Question

in the continuous case, why can't one find the probability of a specific value in the normal distribution?

Answer 1

Solution: The normal distribution is the distribution of a continuous random variable. We know that the continuous random variable takes an infinite number of possible values. Therefore, the continuous random variable in a normal distribution is always defined over an interval of values and it can not be defined over a specific value because at that time the variable will have a single value which will make it discrete and violating the fundamental property of a Normal distribution as the distribution of a continuous random variable. Hence the probability of a specific value in the normal distribution is always 0.

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