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:

• A. 8
• B. 16
• C. 32
• D. 48

Answer 1

The Correct Option is C

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.