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Sagot :
Probability of an event is the measure of its chance of occurrence. The mean of the given probability distribution is 3
How to calculate the expectation(also called mean) of a discrete random variable?
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:
[tex]E(X) = \sum_{i=1}^n( f(x_i) \times x_i)[/tex]
(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:
[tex]\begin{array}{cc}x&P(X = X)\\1&0.1\\2&0.2\\3&0.4\\4&0.2\\5&0.1\end{array}[/tex]
Using the aforesaid definition, we get the mean of random variable X as:
[tex]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[/tex]
Thus, the mean of the given probability distribution is 3
Learn more about expectation of a random variable here:
https://brainly.com/question/4515179
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