The expected value of the discrete random variable x is calculated by multiplying each possible value by its probability and summing up the results. In this case, the closest option to the calculated value is 1.9. It's important to note that if the provided options are different from the calculation, there may be a typo or missing information.
The correct answer to the given question is option B.
To find the expected value of the discrete random variable x, you use the formula E(X) = μ = Σ xP(x), where x represents the values that the random variable can take on, and P(x) is the probability of x occurring.
Given that the values of x range from 0 to 5, and the respective probabilities (expressed as fractions with a denominator of 50) are as follows: P(0) = 2/50, P(1) = 11/50, P(2) = 23/50, P(3) = 9/50, P(4) = 4/50, and P(5) = 1/50, we can calculate the expected value.
To do so, we multiply each value of x by its respective probability and sum those products:
E(X) = (0)(2/50) + (1)(11/50) + (2)(23/50) + (3)(9/50) + (4)(4/50) + (5)(1/50)
Carrying out the multiplication and addition gives us:
E(X) = 0 + 0.22 + 0.92 + 0.54 + 0.32 + 0.10 = 2.1
However, this is not one of the provided options. It's possible there's a typo in the options or that the table provided is incomplete. In the context of the student's question, the closest option to the calculated expected value is 1.9 (Option B).