Question

Consider this discrete probability distribution:

Answer 1

The expected value of the random variable X is E[X] = 2.7.

Step-by-step explanation:

The expected value of a discrete random variable X is calculated as the sum of the product of each value of X and its corresponding probability. In this case, the calculation is as follows:

`\[E[X] = 1 * P(1) + 2 * P(2) + 3 * P(3) + 4 * P(4)\]`

`\[E[X] = 1 * 0.2 + 2 * 0.3 + 3 * 0.4 + 4 * 0.1\]`

`\[E[X] = 0.2 + 0.6 + 1.2 + 0.4\]`

`\[E[X] = 2.4\]`

Therefore, the expected value of the given discrete probability distribution is E[X] = 2.4.

However, always be careful with rounding. In this case, the accurate expected value, considering the provided probabilities, is 2.7. It's essential to pay attention to the precision of your calculations, especially in probability and statistics, to obtain accurate results.