This is the statistical shorthand notation for? X ∼ N (μX, σX)

This is the statistical shorthand notation for? X ∼ N (μX, σX)

• A. The variance of X
• B. The distribution of exponential random variable
• C. how a normal random variable is distributed
• D. The mean of X

Answer: (C)

This notation tells you that X is a normally distributed random variable, with its center at μX and its spread described by σX. The tilde with N indicates the normal distribution family, and the two parameters specify its mean and standard deviation (spread). This is why it encapsulates how a normal random variable is distributed. It’s not just the variance, which would be a single number and often written with a squared parameter, nor is it a statement about an exponential distribution, nor simply about the mean. The two-parameter normal form communicates both the type of distribution and its location (mean) and dispersion (standard deviation).

This notation tells you that X is a normally distributed random variable, with its center at μX and its spread described by σX. The tilde with N indicates the normal distribution family, and the two parameters specify its mean and standard deviation (spread). This is why it encapsulates how a normal random variable is distributed.

It’s not just the variance, which would be a single number and often written with a squared parameter, nor is it a statement about an exponential distribution, nor simply about the mean. The two-parameter normal form communicates both the type of distribution and its location (mean) and dispersion (standard deviation).