Question: Q2. (Write down the measurement unit when applicable and correct your answers to 4 decimal places.) According to the guideline from Dental Association, a dentist

Q2. (Write down the measurement unit when applicable and correct your answers to 4 decimal places.) According to the guideline from Dental Association, a dentist can use up to a maximum of 5 times of nitrous oxide ("laughing gas") in a single treatment. Let X be the number of times of nitrous oxide being used by a dentist in a single treatment. The probability distribution of X is as follows: x 0 1 2 3 4 5 P(X = x) 0.02 0.14 0.36 0.27 0.16 0.05

(a) Find the expectation of X. (2 marks)

(b) Find the variance of X. (2 marks)

(c) A researcher is reviewing reports of 5 independent treatments conducted by this dentist. What is the probability that among the 5 treatments, exactly 2 of them have used nitrous oxide for 0 or 1 time?

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