Explanation:
For a continuous uniform distribution over the interval \([a, b]\):
(a) The mean (\(\mu\)) is given by the average of the two endpoints:
\[ \mu = \frac{a + b}{2} \]
Substitute the values:
\[ \mu = \frac{2.3 + 5.0}{2} \]
Calculate to find the mean.
(b) The variance (\(\sigma^2\)) is given by the formula:
\[ \sigma^2 = \frac{(b - a)^2}{12} \]
Substitute the values:
\[ \sigma^2 = \frac{(5.0 - 2.3)^2}{12} \]
Calculate to find the variance.
(c) To find \(P(X < 3.9)\), where \(X\) is the random variable with a continuous uniform distribution, you can use the formula:
\[ P(X < 3.9) = \frac{x - a}{b - a} \]
Substitute the values:
\[ P(X < 3.9) = \frac{3.9 - 2.3}{5.0 - 2.3} \]
Calculate to find the probability.
Feel free to provide specific values, and I can help with the calculations.