The random variable X has a probability density function given by: Ske-x, (o, 0s xs1; f(x) = otherwise. Then k is equal to: k = The above None of these k = k=e e4-1 The above The above

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Chapter1: Combinatorial Analysis
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The random variable X has a probability density function given by:

\[
f(x) = 
  \begin{cases} 
   ke^{-x}, & 0 \leq x \leq 1; \\
   0, & \text{otherwise}.
  \end{cases}
\]

Then \( k \) is equal to:

1. \( k = \frac{e^2}{e^2 - 1} \)  
   - Option: The above

2. (No option provided; placeholder remains blank)
   - Option: None of these

3. \( k = \frac{e}{e - 1} \)  
   - Option: The above

4. \( k = \frac{e}{e^4 - 1} \)  
   - Option: The above

Each option is followed by a radio button with the text "The above" or "None of these" to select the correct answer.
Transcribed Image Text:The random variable X has a probability density function given by: \[ f(x) = \begin{cases} ke^{-x}, & 0 \leq x \leq 1; \\ 0, & \text{otherwise}. \end{cases} \] Then \( k \) is equal to: 1. \( k = \frac{e^2}{e^2 - 1} \) - Option: The above 2. (No option provided; placeholder remains blank) - Option: None of these 3. \( k = \frac{e}{e - 1} \) - Option: The above 4. \( k = \frac{e}{e^4 - 1} \) - Option: The above Each option is followed by a radio button with the text "The above" or "None of these" to select the correct answer.
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