A random variable x has the following probability distribution:
x f(x)
0 0.08
1 0.17
2 0.45
3 0.25
4 0.05
To find the expected value of a random variable, you need to multiply each value of the random variable by its corresponding probability and then sum up these values.
In this case, the random variable is x and it has values 0, 1, 2, 3, and 4 with their corresponding probabilities 0.08, 0.17, 0.45, 0.25, and 0.05, respectively.
To find the expected value, you can use the formula:
E(x) = x1 * f(x1) + x2 * f(x2) + ... + xn * f(xn)
where E(x) represents the expected value and x1, x2, ..., xn are the values of the random variable, and f(x1), f(x2), ..., f(xn) are their corresponding probabilities.
Let's calculate the expected value step-by-step:
Expected Value = (0 * 0.08) + (1 * 0.17) + (2 * 0.45) + (3 * 0.25) + (4 * 0.05)
Expected Value = 0 + 0.17 + 0.90 + 0.75 + 0.20
Expected Value = 2.07
Therefore, the expected value of the random variable x is 2.07.