Find the Expected Value and Variance for the Random Variable $f ( x ) = 12 x ^ { 2 } ( 1 - x )$

question 1

Short Answer

Find the expected value and variance for the random variable whose probability density function is $f ( x ) = 12 x ^ { 2 } ( 1 - x )$ 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:

Dupp (S2)

The sound made by the heart's valves closing in the cardiac cycle, often associated with the splitting or duplication of the second heart sound.

Muscle Fiber Striations

The visible lines seen in skeletal and cardiac muscle fibers, resulting from the arrangement of actin and myosin filaments.

Electrical Junctions

Specialized connections between cells that allow for the direct transfer of ions and small molecules, enabling electrical communication.

Intercalated Discs

Specialized structures in cardiac muscles that connect cardiac muscle cells to each other, facilitating synchronized contraction of the heart.