Question

A random variable \( X \) has the following distribution:

Then the ratio between \( k \) and \( P(X \lt 3) \) is:

• A. \( 1:1 \)
• B. \( 1:2 \)
• C. \( 1:3 \)
• D. \( 3:1 \)

Hint:

You don't always need the actual value of \( k \) to find ratios. Since both terms depend linearly on \( k \), it cancels out during division.

Answer 1

The Correct Option is C

Step 1: Solve for \( k \) numerically.
With probabilities \( k, 2k, 3k, 4k \) for \( X = 1,2,3,4 \), the total must be 1, so \( 10k=1 \) and \( k = 0.1 \).

Step 2: List the actual probability values.
This gives \( P(X=1)=0.1 \), \( P(X=2)=0.2 \), \( P(X=3)=0.3 \), \( P(X=4)=0.4 \).

Step 3: Compute the ratio directly with numbers.
\[ P(X \lt 3) = 0.1+0.2 = 0.3 \] \[ k : P(X \lt 3) = 0.1 : 0.3 = 1:3 \] \[ \boxed{1:3} \]