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suppose x has a continuous uniform distribution over the interval [2.3, 5.0]. round your answers to 3 decimal places. (a) determine the mean of x. (b) determine the variance of x. (c) what is < 3.9)?

User Nethero
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1 Answer

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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.

User Chemik
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