# Probability Questions and Answers – Random Variables – Set 2

This set of Probability Multiple Choice Questions & Answers (MCQs) focuses on “Random Variables – Set 2”.

1. A fair dice is rolled 6 times. What is the probability of seeing 4?
a) 4/6
b) 3/6
c) 0
d) 1/6

Explanation: The dice has 6 outcomes – {1, 2, 3, 4, 5, 6}. Since it is a fair dice, all six outcomes are equally likely. Hence the probability of seeing anyone digit is equal to (1/number of outcomes) i.e. 1/6.

2. How many types of random variables are there?
a) One
b) Five
c) Two
d) Three

Explanation: There are three types of random variables – discrete, continuous and mixed. The discrete variable takes a specific finite or countable value from a list of given values. A continuous variable can take any numerical value in a particular interval. A mixed variable is neither fully discrete nor everywhere continuous.

3. A random variable does not always require being measurable.
a) True
b) False

Explanation: Random variables have to be measurable. Only then, a probability can be attached to its potential outcomes.

4. It is advisable to represent non-numerical outcomes of a random variable using numerical values.
a) True
b) False

Explanation: Assigning probability to numerical outcomes is easier. Hence assigning numerical values to outcomes of non-numerical nature can help in the calculation.

5. A coin toss is an example of __________ random variable.
a) continuous
b) discrete
c) either continuous or discrete
d) mixed

Explanation: The possible outcomes of a coin toss are finite – heads or tails. Since the number of outcomes is distinctively two, it is a discrete random variable.

6. The weather can be sunny, cloudy or rainy. All three are equally likely. What is the probability that the weather is sunny?
a) 1
b) 0
c) 1/3
d) 2/3

Explanation: There are 3 recognized weather types (outcomes) and all are equally likely. Hence any one of them can occur at a probability of (1/number of outcomes) i.e. 1/3.

7. How many types of discrete random variables are there?
a) Two
b) Three
c) Four
d) Five

Explanation: There are two types of discrete random variables – numerical and non-numerical. A fair dice is an example of a numerical random variable as it has six outcomes, all of whom are numerical – {1, 2, 3, 4, 5, 6}. A coin toss is an example of a non-numerical random variable as it has two outcomes, both being non-numerical – {head, tails}.

8. Let Y = X2. X takes the following values {-2, -1, 0, 1, 2}. What is the probability of finding Y = 4?
a) 1/5
b) 0
c) 4/5
d) 2/5

Explanation: Y = 4 when X = 2 or X = -2. Now, X has five possible outcomes, and two of them will lead to Y being 4. Hence the probability is (number of likely outcomes/total number of outcomes) i.e. 2/5.

9. Y = X for 0 < X < 1. Y is _____ random variable.
a) mixed
b) discrete
c) continuous
d) non-numerical

Explanation: Y can take any value between 0 and 1, except for 0 and 1. Hence, it is a continuous random variable. Y is numerical as it takes only numerical values. Y is never discrete as there is always a particular value of Y between any two other values (between 0.1 and 0.2 there can be infinite values of Y ranging from 0.01 to 0.190999999 to 0.1999).

10. The full form of CDF in relation to probability theory is __________
a) Continuous Distribution Function
b) Cumulative Distribution Function
c) Cumulative Distributive Function
d) Continuous Distributive Function

Explanation: The correct answer is the cumulative distribution function. It gives the probability of finding X less than or equal to a certain value.

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