A Random Variable Has Probability Density Function F(x) = 30 $x ^ { 2 }$

question 76

Multiple Choice

A random variable has probability density function f(x) = 30 $x ^ { 2 }$ (1 - x $) ^2$
(0 ≤ x ≤ 1) . Compute its cumulative distribution F(x) .

• A) 10 \(x ^ { 3 }\) - \(15 x ^ { 4 }\) + 6 \(x ^ { 5 }\) + 1
• B) 10 \(x ^ { 3 }\) - 15 \(x ^ { 4 }\) + 6 \(x ^ { 5 }\)
• C) 30x(1 - x)
• D) 30 \(x ^ { 2 }\) - 60 \(x ^ { 3 }\) + \(30 x ^ { 4 }\)
• E) none of these

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Definitions:

Somatic Portion

Refers to the part of an organism's body that is not involved in reproduction, including cells that make up tissues, organs, and systems.

Peripheral Nervous

The portion of the nervous system lying outside the brain and spinal cord, which includes nerves branching off from the brainstem and spinal cord to the rest of the body.

Sensory Nerves

Nerves responsible for conveying sensory information from the body's periphery to the central nervous system, including touch, pain, temperature, and position sense.

Cerebrum

The largest part of the brain, responsible for voluntary activities, intelligence, learning, and memory.