Question Video: Finding the Probability for a Given Value of a Discrete Random Variable Mathematics

Let 𝑋 denote a discrete random variable which can take the values βˆ’2, 2, 4 and 5ive. Given that P(𝑋 = βˆ’2) = 0.15, P(𝑋 = 2) = 0.43, and P(𝑋 = 4) = 0.25, find P(𝑋 > 2).

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Video Transcript

Let 𝑋 denote a discrete random variable which can take the values negative two, two, four, and five. Given that the probability 𝑋 equals negative two is 0.15, the probability 𝑋 equals two is 0.43, and the probability 𝑋 equals four is 0.25, find the probability 𝑋 is greater than two.

In this question, we’re not asked to determine the probability that our random variable is equal to a particular value, but rather the probability that it is greater than a given value. This may look a little confusing at first, but the key to remember is that a discrete random variable can only take the values in its range and no others. Let’s begin by representing information in the question using a table. We have the values in the range of our discrete random variable in the top row and the corresponding probabilities in the second row.

Now, we do have a missing probability, the probability that 𝑋 equals five, but we’ll worry about that later if necessary. We want to find the probability that 𝑋 is greater than two. Now remember that our discrete random variable can only take the values in its range. For 𝑋 to be strictly greater than two, this means that it must either take the value four or the value five. There are no other values it can take. The probability 𝑋 is greater than two then is equal to the sum of the probability 𝑋 equals four and the probability 𝑋 equals five.

Now remember, we don’t know the probability 𝑋 equals five, although we can easily calculate it by remembering that the sum of all probabilities in the distribution must be equal to one. Instead, a slightly easier way may be to recall that the probability 𝑋 is greater than two will be equal to one minus the probability 𝑋 is less than or equal to two. So, instead, we can just subtract the probabilities for 𝑋 equaling negative two and 𝑋 equaling two from one, one minus 0.15 and 0.43, which is equal to 0.42.

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