1. Based on her past experience, a professor knows that the probability distribu
ID: 3061248 • Letter: 1
Question
1. Based on her past experience, a professor knows that the probability distribution of the number of students who come to her office hours, is as follows P(X=x) | 0.1 | 0.2 | 0.5 | 0.15 | 0.05 a) What is the probability that three students that come to office hours? (1 point) b) What is the probability that at least 2 students come to office hours? (1 point) c) What is the expected number of students that will come during office hours? (2 points) d) What is the variance of this probability distribution? (3 points)Explanation / Answer
The given table is:
a) The probability that three students come to office
P(X = 3) = 0.15.
b) The probability that atleast two students come to office
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4)
= 0.5 + 0.15 + 0.05
= 0.7.
c) Expected number of students
= x p(x)
= 0 * 0.1 + 1 * 0.2 + 2 * 0.5 + 3 * 0.15 + 4 * 0.05
= 1.85
d) Variance
= x2 p(x) - (x p(x))2
= 0 * 0.1 + 1 * 0.2 + 4 * 0.5 + 9 * 0.15 + 16 * 0.05 - 1.85 * 1.85
= 0.9275.
x 0 1 2 3 4 P(X = x) 0.1 0.2 0.5 0.15 0.05Related Questions
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