Let X Be a Continuous Random Variable with Density Function $f ( X ) = \left\{ \begin{array} { l l } c \cdot e ^ { - c X } & \text { if } x \geq 0 \\0 & \text { otherwise }\end{array} \right.$

question 79

Multiple Choice

Let X be a continuous random variable with density function $f ( X ) = \left\{ \begin{array} { l l } c \cdot e ^ { - c X } & \text { if } x \geq 0 \\0 & \text { otherwise }\end{array} \right.$ If the median of this distribution is $\frac { 1 } { 3 }$ , then c is:

• A) \(\frac { 1 } { 3 }\) \(\ln \frac { 1 } { 2 }\)
• B) \(\frac { 1 } { 3 }\) \(\ln 2\)
• C)2 \(\ln \frac { 3 } { 2 }\)
• D) \(3 \ln 2\)
• E)3
• F) \(\frac { 1 } { 3 }\)
• G) \(2 \cdot \frac { \ln 3 } { \ln 2 }\)
• H)3 \(\ln \frac { 1 } { 2 }\)

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Definitions:

Hasty Generalization

Drawing a broad conclusion from a small sample or isolated instances.

Accident Fallacy

Refers to a logical fallacy that involves applying a general rule to a specific case it does not apply to, often leading to erroneous conclusions.

Slippery Slope Argument

A logical fallacy that assumes a relatively small first step will lead to a chain of related events culminating in some significant effect, often negative.

Consequences

The results or outcomes that naturally follow from a person's actions or a set of circumstances.