Find the Area of That Part of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4 z$

question 34

Short Answer

Find the area of that part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4 z$ that lies inside the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ .

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Definitions:

Variance

A measure of the dispersion or spread of a set of data points, indicating how much the data deviate from their mean.

Random Variable

A variable that can take on numerical results stemming from a random event.

Poisson Random Variable

A variable that represents the number of events occurring in a fixed interval of time or space, under conditions of a constant mean rate and independence.

Discrete Random Variable

A variable that can take on a countable number of distinct values, often used to model scenarios where outcomes are distinct.