Find the Expected Value and Variance for the Random Variable $f ( x ) = 3 x ^ { 2 }$

question 4

Short Answer

Find the expected value and variance for the random variable whose probability density function is $f ( x ) = 3 x ^ { 2 }$ 0 ≤ x ≤ 1.
Enter just two reduced fractions (unlabeled) in the order E(X), Var(X) separated by a comma.

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Definitions:

Profit-Maximizing

A process or strategy aiming to achieve the highest possible profits from business operations.

Marginal Revenue Curve

A graphical representation showing how marginal revenue varies as output quantity changes, typically downward sloping for firms in competitive markets.

Economic Profit

The difference between total revenue and total costs, including both explicit and implicit costs, representing a firm's net gain.

Marginal Cost

The cost increase associated with the production of an extra unit of a product or service.