Probability Distribution MCQs | Probability Distribution Multiple Choice Questions and Answers

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Questions
1 When do the conditional density functions get converted into the marginally density functions ?
A Only if random variables exhibit statistical independency
B If random variables do not exhibit deviation from its mean value
C Only if random variables exhibit statistical dependency
D Only if random variables exhibit deviation from its mean value

Answer: Only if random variables exhibit statistical independency
2 What would be the probability of an event ‘G’ if H denotes its complement, according to the axioms of probability?
A P (G) = P (H)
B P (G) = 1 + P (H)
C P (G) = 1 / P (H)
D P (G) = 1 – P (H)

Answer: P (G) = 1 – P (H)
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3 A variable that can assume any value between two given points is called
A Uncertain random variable
B Irregular random variable
C Discrete random variable
D Continuous random variable

Answer: Continuous random variable
4 Out of the following values, which one is not possible in probability ?
A P(x) = – 0.5
B P(x) = 0.5
C P(x) = 1
D ∑ x P(x) = 3

Answer: P(x) = – 0.5
5 Which of the following statements is not correct concerning the probability distribution of a continuous random variable?
A the vertical coordinate is the probability density function
B the range of the random variable is found on the x-axis
C the area under the curve between points a and b represents the probability that X = a
D the total area represented under the curve will equal 1

Answer: the area under the curve between points a and b represents the probability that X = a
6 In a popular shopping centre, the waiting time for an ABSA ATM machine is found to be uniformly distributed between 1 and 5 minutes. What is the probability of waiting between 2 and 4 minutes to use the ATM?
A 0.50
B 0.40
C 0.20
D 0.75

Answer: 0.50
7 Which of the following statements is correct?
A The mean of the Poisson distribution (with parameter μ) equals the mean of the Exponential distribution (with parameter λ) only when μ = λ = 1
B The Uniform distribution is a discrete probability distribution
C The Exponential distribution is continuous and defined over the interval (-∞, ∞)
D The Binomial distribution has equal mean and variance only when p = 0.5

Answer: The mean of the Poisson distribution (with parameter μ) equals the mean of the Exponential distribution (with parameter λ) only when μ = λ = 1
8 A larger standard deviation for a normal distribution with an unchanged mean indicates that the distribution becomes:
A flatter and wider
B more skewed to the left
C narrower and more peaked
D a change in the standard deviation does not change the shape of the distribution

Answer: flatter and wider
9 Which of the following mentioned standard Probability density functions is applicable to discrete Random Variables ?
A Poisson Distribution
B Exponential Distribution
C Gaussian Distribution
D Rayleigh Distribution

Answer: Poisson Distribution
10 Mutually Exclusive events
A Does not contain any common sample point
B Contain all common sample points
C Does not contain any sample point
D Contain all sample points

Answer: Does not contain any common sample point
11 A table with all possible value of a random variable and its corresponding probabilities is called
A Probability Distribution
B Cumulative distribution function
C Probability Mass Function
D Probability Density Function

Answer: Probability Distribution
12 If a variable can certain integer values between two given points is called
A Discrete random variable
B Uncertain random variable
C Continuous random variable
D Irregular random variable

Answer: Discrete random variable
13 Which of the following is not a characteristic of the normal distribution?
A the mean is always zero
B the area under the curve equals one
C the mean, median and mode are equal
D it is a symmetrical distribution

Answer: the mean is always zero
14 Which of the following do the normal distribution and the exponential density function have in common?
A both are symmetrical distributions
B both approach zero as x approaches infinity
C both approach infinity as x approaches infinity
D both are bell-shaped

Answer: both approach zero as x approaches infinity
15 Which of the following distributions is suitable to measure the length of time that elapses between the arrival of cars at a petrol station pump?
A Exponential
B Normal
C Uniform
D Binomial

Answer: Exponential
16 A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all the questions randomly by guessing the answer to each question. Which of the following probability distributions can be used to calculate the student’s chance of getting at least 20 questions right?
A Uniform distribution
B Exponential distribution
C Poisson distribution
D Binomial distribution

Answer: Binomial distribution
17 Which of the following statements is/are true regarding the normal distribution curve?
A it is asymptotic in that each end approaches the horizontal axis but never reaches it
B it is symmetrical
C its mean, median and mode are located at the same point
D all of the above statements are true

Answer: all of the above statements are true
18 Which of the following cannot generate a Poisson distribution?
A The number of customers arriving at a petrol station
B The number of cars arriving at a parking garage in a one-hour time interval
C The number of misprints per page
D The number of telephone calls received in a ten-minute interval

Answer: The number of customers arriving at a petrol station
19 Which of the following statements regarding the probability density function, f(x), of the uniform distribution is correct?
A the density function is constant for all values that X can assume
B the height of the density function differs for different values of X
C the density function increases as the values of X increase
D the density function is roughly “bell-shaped”

Answer: the density function is constant for all values that X can assume
20 Which of the following is not a correct statement?
A the mean of the exponential distribution is the inverse of the mean of the Poisson
B the exponential distribution describes the Poisson process as a continuous random variable
C the area under the curve for an exponential distribution equals 1
D none of the above

Answer: the mean of the exponential distribution is the inverse of the mean of the Poisson

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