Work out the expected value of the random variable 𝑋 whose probability distribution is shown.
The expected value of a discrete random variable is the weighted average of the values of the variable. Essentially, it is calculated by finding the sum of the products of every possible value of 𝑋 and its associated probability, probability of 𝑋, 𝑝 of 𝑋. So we have a summation, so that means we’re going to add together a few things. We will plug in the values for 𝑥 — the random variable 𝑋 which is one, two, three, and four — and then we’ll also plug in the associated probability of 𝑋, which are the values on the 𝑦-axis.
So our first value of 𝑥 being one, the probability of that would be 0.1. So next, we take two times 0.3 and then three times 0.4. And we take four times 0.2. And now we multiply. One times 0.1 is 0.1, two times 0.3 is 0.6, three times 0.4 is 1.2, and four times 0.2 is 0.8. Now we add all-all of this together, and we get 2.7.
So the expected value of our random variable 𝑋 is 2.7.