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(ELEC2600)(s)midterm~htang^_21247.pdf
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SECTION I: Multiple Choice [10 Marks]

Notes:
. For each multiple-choice question below, select only ONE answer.

[1 Mark Per Question]

1. For a discrete random variable, X, which of the following statements is not true?

a) We can evaluate all moments of X solely based on the probability mass function

b) The standard deviation of X has the same units as the mean

c) All moments of X are non-negative

d) The conditional mean and variance of X (conditioned on some event A) are examples of moments.

e) Trellis diagrams, which represent the decoder of a Trellis Coded Modulation communication system, implement successive products of conditional probabilities.

2. Which of the following statements about conditional probability is not true?

a) Conditioning always increases the probability of an event

b) Conditioning may increase or decrease the probability of an event

c) Conditioning changes the effective sample space of the experiment

d) The Total Theorem of Probability allows one to compute unconditional probabilities by combining conditional probabilities

3. Assume that we select balls from an urn, at random. From the following selection methods, which method does not lead to equally-probable events?

a) With replacement with ordering

b) Without replacement with ordering

c) With replacement without ordering

d) Without replacement without ordering

4. If two events have non-zero probabilities and are mutually exclusive, then they:

a) Must be independent

b) Cannot be independent

c) Can be independent or not independent

d) Always form a partition

e) Can never form a partition

5. In a sequential experiment, if the outcome of the nth sub-experiment sn depends only on that of the (n-1)th sub-experiment sn-1, which of the following statements is not true?

a) It is a dependent sequential experiment

b)

c) sn and sn-2 are independent

d) For a given sn-1, sn and sn-2 are independent

e) None of the above (i.e., they are all true)

6. Which of the following statements about equivalent events is not true?

a) If two outcomes map to the same number, they belong to the same equivalent event

b) If two events are equivalent, they have the same probability

c) A random variable defined on a discrete sample space must be a discrete random variable. Vice versa.

d) The equivalent events that correspond to all possible values of a discrete random variable form a partition of the underlying sample space

e) None of the above (i.e., they are all true)

7. If the CDF of a random variable, X, has discrete jumps, then:

a) X must be a discrete random variable

b) X can be a continuous random variable.

c) X can be either discrete or continuous

d) X can be both discrete and continuous

e)