A die is loaded in such a way that an even number is twice likely to occur as an odd number. If the die is tossed twice, find the probability distribution of the random variable X representing the perfect squares in the two tosses.

Explanation

To solve the problem step-by-step, we will follow the outlined process to find the probability distribution of the random variable \( X \) representing the perfect squares when a loaded die is tossed twice.

### Step 1: Define the probabilities of outcomes on the die
We know that the die is loaded such that an even number is twice as likely to occur as an odd number. Let's denote the probability of rolling an odd number (1, 3, or 5) as \( p \). Therefore, the probabilities for the even numbers (2, 4, or 6) will be \( 2p \).

### Step 2: Set up the equations for total probability
The total probability for all outcomes on a die must equal 1. The outcomes are:
- Odd numbers: 1, 3, 5 (each with probability \( p \))
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