Question

Let X~N(23,4)

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 \( X = 4 \)