Probability of an event is the measure of its chance of occurrence. The mean of the given probability distribution is 3
<h3>How to calculate the expectation(also called mean) of a discrete random variable?</h3>
Expectation can be taken as a weighted mean, weights being the probability of occurrence of that specific observation.
Thus, if the random variable is X, and its probability mass function is given as: f(x) = P(X = x), then we have:
![E(X) = \sum_{i=1}^n( f(x_i) \times x_i)](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%5Csum_%7Bi%3D1%7D%5En%28%20f%28x_i%29%20%5Ctimes%20x_i%29)
(n is number of values X takes)
For the given case, we have:
X = project grade (from 1 to 5, thus, 1, 2,3,4, or 5 as its values.)
The probability distribution of X is given as:
![\begin{array}{cc}x&P(X = X)\\1&0.1\\2&0.2\\3&0.4\\4&0.2\\5&0.1\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcc%7Dx%26P%28X%20%3D%20X%29%5C%5C1%260.1%5C%5C2%260.2%5C%5C3%260.4%5C%5C4%260.2%5C%5C5%260.1%5Cend%7Barray%7D)
Using the aforesaid definition, we get the mean of random variable X as:
![E(X) = \sum_{i=1}^n( f(x_i) \times x_i)\\\\E(X) = 1 \times 0.1 + 2 \times 0.2 + 3 \times 0.4 + 4 \times 0.2 + 5 \times 0.1\\E(X) = 0.1 + 0.4 + 1.2 + 0.8+0.5 = 3](https://tex.z-dn.net/?f=E%28X%29%20%3D%20%5Csum_%7Bi%3D1%7D%5En%28%20f%28x_i%29%20%5Ctimes%20x_i%29%5C%5C%5C%5CE%28X%29%20%3D%201%20%5Ctimes%200.1%20%2B%202%20%5Ctimes%200.2%20%2B%203%20%5Ctimes%200.4%20%2B%204%20%5Ctimes%200.2%20%2B%205%20%5Ctimes%200.1%5C%5CE%28X%29%20%3D%200.1%20%2B%200.4%20%2B%201.2%20%2B%200.8%2B0.5%20%3D%203)
Thus, the mean of the given probability distribution is 3
Learn more about expectation of a random variable here:
brainly.com/question/4515179