The function in the given table is a probability function of a discrete random variable 𝑋. Find the value of 𝑎.
So we’ve been given a table containing the possible values of 𝑥 and their given probabilities. Now in order to find 𝑎, we just need to use the fact that the sum of all probabilities has to equal one.
So in order to find 𝑎, we simply take all our probabilities, add them together, and put them equal to one. This gives us two 𝑎 plus 0.3 plus 0.3 plus 𝑎 plus 𝑎 is equal to one. And now this can be simplified to four 𝑎 plus 0.6 equals one.
Now we subtract 0.6 from either side. And this leaves us with four 𝑎 is equal to 0.4. And finally, we divide both sides by four. This gives us a final answer of 𝑎 is equal to 0.1.