Question:

The probability distribution of a discrete random variable \(X\) is given below :
\(X\)\(2\)\(3\)\(4\)\(5\)
\(P(X)\)\(\frac5k\)\(\frac7k\)\(\frac9k\)\(\frac{11}{k}\)

then the value of k is:

Updated On: May 12, 2025
  • 8
  • 16
  • 32
  • 48
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The Correct Option is C

Solution and Explanation

To solve for the value of \(k\), we use the property that the sum of all probabilities for a discrete random variable must equal to 1. Therefore, we have the equation:
\(\frac{5}{k}+\frac{7}{k}+\frac{9}{k}+\frac{11}{k}=1\)
Combine the terms in the numerator:
\(\frac{5+7+9+11}{k}=1\)
Simplifying the numerator:
\(\frac{32}{k}=1\)
Solving for \(k\), we multiply both sides by \(k\) to eliminate the fraction:
\(32=k\)
Therefore, the value of \(k\) is 32.
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