Question

Find the value of \( k \).

Hint:

In probability distributions, the sum of all probabilities must be equal to 1. Use this property to find unknown parameters.

Answer 1

Step 1: The total probability must sum to 1: \[ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1. \] Step 2: Substitute the given probability values: \[ P(X = 0) = 0.1, \quad P(X = 1) = k(1), \quad P(X = 2) = k(2), \] \[ P(X = 3) = k(5 - 3), \quad P(X = 4) = k(5 - 4). \] Step 3: Form the equation: \[ 0.1 + k(1) + k(2) + k(2) + k(1) = 1. \] Step 4: Simplify the equation: \[ 0.1 + 6k = 1. \] Step 5: Solve for \( k \): \[ k = \frac{1 - 0.1}{6} = \frac{0.9}{6} = 0.15. \]