MATH254: Tutorial Exercise for Week 2
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MATH254: Tutorial Exercise for Week 2
1. For each of the following statements, say whether true or false. For false statements, give the correct
version of the statement.
Let A and B be two events.
(i) A\B = A n (A u B).
(ii) Pr(A n B) = Pr(A) x Pr(B) if A, B are independent.
(iii) Pr(A u B) = Pr(A) + Pr(B) if A, B are independent.
(iv) In a sequence of n independent identical trials, each of which results in either ‘success’ or ‘failure’, with probability θ of success, the number of successes follows a Bernoulli distribution.
2. In five independent tosses of an unbiased coin, find (i) the probability that the total number of heads is even; (ii) the probability that there are exactly five heads. (Note: zero is even.)
3. A discrete random variable X has possible values -2, 1, 3, 4 with probabilities satisfying Pr(X = -2) = Pr(X = 1) = 2 Pr(X = 3) = 3 Pr(X = 4).
Find the probability mass function and the (cumulative) distribution function of X .
2022-03-07