The probability distribution of discrete random variable X is given below
`{:(x,2,3,4,5),(P(x),5/K,7/k,9/k,11/k):}`
find the value of K.

Answer

To find the value of \( K \) in the given probability distribution of the discrete random variable \( X \), we can follow these steps:

### Step 1: Write down the probability distribution
The probability distribution is given as:
- \( P(X=2) = \frac{5}{K} \)
- \( P(X=3) = \frac{7}{K} \)
- \( P(X=4) = \frac{9}{K} \)
- \( P(X=5) = \frac{11}{K} \)

### Step 2: Set up the equation for total probability
The sum of all probabilities must equal 1:
\[ P(X=2) + P(X=3) + P(X=4) + P(X=5) = 1 \]

Substituting the probabilities:
\[ \frac{5}{K} + \frac{7}{K} + \frac{9}{K} + \frac{11}{K} = 1 \]

### Step 3: Combine the fractions
Since all terms have a common denominator \( K \), we can combine them:
\[ \frac{5 + 7 + 9 + 11}{K} = 1 \]

### Step 4: Calculate the sum of the numerators
Now, calculate the sum of the numerators:
\[ 5 + 7 + 9 + 11 = 32 \]

### Step 5: Set up the equation
Now we have:
\[ \frac{32}{K} = 1 \]

### Step 6: Solve for \( K \)
To find \( K \), we can rearrange the equation:
\[ 32 = K \]

Thus, the value of \( K \) is:
\[ K = 32 \]

### Final Answer
The value of \( K \) is \( 32 \).

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