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:

Adverse Selection

A situation where asymmetric information results in high-risk individuals being more likely to select into or remain in a contract designed for low-risk individuals, affecting insurance markets and other transactional relationships.

Asymmetric Information

A situation in which one party to a transaction has more or superior information compared to another.

Moral Hazard

The situation where one party is more likely to take risks because they do not bear the full consequences of those risks.

Hidden Action

A situation in contract theory and economics where one party's action is not observed or cannot be monitored by another, potentially leading to moral hazard.