Determine the Probability of an Outcome of the Probability Density $f ( x ) = 4 x ^ { 3 }$

question 44

Short Answer

Determine the probability of an outcome of the probability density function $f ( x ) = 4 x ^ { 3 }$ being between $\frac { 1 } { 4 } \text { and } \frac { 1 } { 2 }$ where $0 \leq x \leq 1$ .
Enter just a reduced fraction.

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Definitions:

Interdependence

A relationship between entities where each depends on the other, often leading to mutual influence or reliance.

Mutual Influence

Mutual influence is the reciprocal effect individuals or groups have on each other's attitudes, behaviors, or opinions, often leading to changes or adjustments in response to the interaction.

True Group

A collection of individuals who interact with one another, share common goals, and see themselves as part of a cohesive unit.

Entitativity

The degree to which a group is perceived as being a coherent and distinct entity, often based on the members' similarity, proximity, and shared goals.