Question 1 [0.5 x 5 = 2.5 mark each]

Consider a random variables X with the following probability distribution:

X -4 0 1 2 P(x) 0.2 0.3 0.4 0.1

Find the following probabilities:

P(x>0)

P(x0)

P(x X 1)

P(x = -2)

P(x = -4)

1. Harvard undergraduates completed the National College Health Assessment Questionnaire in 2003. The number of students self-reporting cigarette smoking habits and/or marijuana use habits are given below:

Marijuana use

Cigarette

smoking Has smoked Never smoked Total 790 1882 2672

The 2 test statistic for this table is 770.6. Is this significant evidence of an association between cigarette smoking and marijuana use? Be sure to include the hypotheses, the degrees of freedom, an estimate for the p-value (or the critical value), and your conclusion in the context of the problem.