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A random variable X has the following di...

A random variable X has the following distribution
`{:(x,1,2,3,4),(P(X=x),c,2c,3c,4c):}`
The value of c is

A

1

B

10

C

`(1)/(10)`

D

`(1)/(5)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the value of \( c \) in the given probability distribution of the random variable \( X \), we will follow these steps: ### Step 1: Write down the probability distribution. The random variable \( X \) has the following distribution: - \( P(X = 1) = c \) - \( P(X = 2) = 2c \) - \( P(X = 3) = 3c \) - \( P(X = 4) = 4c \) ### Step 2: Use the property of probabilities. We know that the sum of all probabilities must equal 1. Therefore, we can write the equation: \[ P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1 \] Substituting the probabilities into the equation gives us: \[ c + 2c + 3c + 4c = 1 \] ### Step 3: Combine like terms. Now, we can combine the terms on the left side: \[ (1 + 2 + 3 + 4)c = 1 \] This simplifies to: \[ 10c = 1 \] ### Step 4: Solve for \( c \). To find \( c \), we divide both sides of the equation by 10: \[ c = \frac{1}{10} \] ### Conclusion: The value of \( c \) is \( \frac{1}{10} \). ---
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