The random variableX has the following continuous probability distribution in the range 0 < x < k - 4 (where k is a positive number) is shown in the coordinate plane with X on the horizontal axis. f(x) k -1.5 3 -- k – 4

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The random variable \( X \) has the following continuous probability distribution in the range \( 0 \leq x \leq k - 4 \) (where \( k \) is a positive number) as shown in the coordinate plane with \( x \) on the horizontal axis.

The graph illustrates the probability density function \( f(x) \). The horizontal axis represents the variable \( x \) ranging from 0 to \( k-4 \). The vertical axis represents the function \( f(x) \). 

The function \( f(x) \) is constant at \( \frac{k}{3} - 1.5 \) for the given range. This is depicted as a horizontal line extending from \( x = 0 \) to \( x = k-4 \). 

The question posed is: What is the median of \( X \)?
Transcribed Image Text:The random variable \( X \) has the following continuous probability distribution in the range \( 0 \leq x \leq k - 4 \) (where \( k \) is a positive number) as shown in the coordinate plane with \( x \) on the horizontal axis. The graph illustrates the probability density function \( f(x) \). The horizontal axis represents the variable \( x \) ranging from 0 to \( k-4 \). The vertical axis represents the function \( f(x) \). The function \( f(x) \) is constant at \( \frac{k}{3} - 1.5 \) for the given range. This is depicted as a horizontal line extending from \( x = 0 \) to \( x = k-4 \). The question posed is: What is the median of \( X \)?
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