A Random Variable X Has Probability Density Function F(x) = $k e ^ { - k x }$

question 87

Multiple Choice

A random variable X has probability density function f(x) = $k e ^ { - k x }$ (x ≥ 1) for some constant k. Suppose that $\operatorname { Pr } ( 1 \leq X \leq 2 ) = \frac { 1 } { 4 }$ , what is the value of k?

• A) \(\frac { 1 } { 2 }\) ln 2
• B) \(\frac { 3 } { 2 }\) ln 2
• C) \(\frac { 1 } { 4 }\)
• D) ln 2
• E) none of these

Analyze and calculate insurance refunds and costs associated with policy cancellations and changes in coverage.

Calculate the monetary outcome of insurance claims considering deductibles, premiums, and coverage limits.

Evaluate the financial impact of differing premium rates and discounts over time.

Understand and apply coinsurance clauses to calculate insurance payouts and policyholder responsibilities after a claim.

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