Question

Let X be the number of students who show up for a professor's office hour on a particular day. Suppose that the pmf of X is p(0) = 0.15, p(1) = 0.10, p(2) = 0.30, p(3) = 0.20, and p(4) = 0.25. a) Draw the corresponding probability histogram. b) What is the probability that at least two students show up?

Answer 1

Explanation:

a) To draw the corresponding probability histogram, we can represent each value of X on the x-axis and their corresponding probabilities on the y-axis. Here is the probability histogram:

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0 1 2 3 4

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The height of each bar represents the probability of the corresponding value of X.

b) To find the probability that at least two students show up, we need to sum the probabilities for X = 2, 3, and 4:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4)

= 0.30 + 0.20 + 0.25

= 0.75

Therefore, the probability that at least two students show up is 0.75 or 75%.