Let X~N(23,4)

Question

Expected value of X =

Standard deviation of X =

Variance of X =

Answer 1

For a normal distribution \( X \sim N(\mu, \sigma^2) \), where \( \mu \) is the mean (expected value) and \( \sigma^2 \) is the variance:

1. The expected value of \( X \) (mean) is: \[ E[X] = \mu = 23 \]

2. The standard deviation of \( X \) is the square root of the variance. Given that the standard deviation is the square root of the variance, and you provided the value of the variance directly as \( 4 \) (which is actually \( \sigma^2 \)): \[ \text{Standard Deviation (} \sigma) = \sqrt{4} = 2 \]

3. The variance of \( X \) is: \[ \text{Variance (} \sigma^2) = 4 \]

To summarize:

• Expected value of \( X = 23 \)
• Standard deviation of \( X = 2 \)
• Variance of \( X = 4 \)