A biased die is used in a game - Leaving Cert Mathematics - Question 2 - 2013

To find the expected value $E(X)$ of the random variable $X$, we use the formula:

$E(X) = ext{Sum of (Value} \times ext{ Probability)}$

Substituting the values from the table:

$E(X) = (1 \times 0.25) + (2 \times 0.25) + (3 \times 0.15) + (4 \times 0.15) + (5 \times 0.10) + (6 \times 0.10)$

Calculating each term:

• For 1: $1 \times 0.25 = 0.25$
• For 2: $2 \times 0.25 = 0.50$
• For 3: $3 \times 0.15 = 0.45$
• For 4: $4 \times 0.15 = 0.60$
• For 5: $5 \times 0.10 = 0.50$
• For 6: $6 \times 0.10 = 0.60$

Now summing these up:

$E(X) = 0.25 + 0.50 + 0.45 + 0.60 + 0.50 + 0.60 = 2.90$

Thus, the expected value of $X$ is 2.90.