MCQs

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Overall MCQs for Reference

The sum of all probabilities in a discrete probability distribution is:
a. 0
b. 1
c. Infinite
d. Undefined
Answer: b. 1sanfoundry
Which distribution models the number of successes in n independent Bernoulli trials?
a. Binomial
b. Poisson
c. Uniform
d. Exponential
Answer: a. Binomialitfeature
The mean of a binomial distribution with n trials and probability p is:
a. np
b. n/p
c. n^p
d. p/n
Answer: a. nptestbook
In Poisson distribution, the expected number of occurrences in an interval is represented by:
a. n
b. λ
c. σ
d. μ
Answer: b. λtestbook
The standard deviation of a normal distribution is denoted as:
a. μ
b. σ
c. λ
d. p
Answer: b. σtestbook
Which distribution is described as symmetric about its mean?
a. Binomial
b. Poisson
c. Normal
d. Exponential
Answer: c. Normaltestbook
The range of a uniform distribution on is:sanfoundry
a. 0–1
b. -∞ to ∞
c. 1–2
d. 0 only
Answer: a. 0–1scribd
What describes the probability mass function (PMF)?
a. For discrete random variable
b. For continuous random variable
c. Only for uniform distribution
d. None of these
Answer: a. For discrete random variabletestbook
If a die is rolled, the probability distribution is:
a. Binomial
b. Uniform
c. Poisson
d. Exponential
Answer: b. Uniformtestbook
For a success probability p in a Bernoulli trial, possible values for the random variable are:
a. {0, 1}
b. {1, 2}
c.sanfoundry
d. {0, 1, 2}
Answer: a. {0, 1}scribd
The variance of a binomial distribution is:
a. np
b. np(1–p)
c. n^2p
d. np^2
Answer: b. np(1–p)testbook
The distribution best suited for modeling rare events:
a. Uniform
b. Binomial
c. Poisson
d. Geometric
Answer: c. Poissontestbook
Probability density function (PDF) is used for:
a. Discrete variables
b. Continuous variables
c. Categorical variables
d. None of these
Answer: b. Continuous variablestestbook
In a geometric distribution, the probability that the first success occurs on the 4th trial is:
a. p^4
b. (1–p)^3 p
c. (1–p)^4 p
d. p (1–p)^4
Answer: b. (1–p)^3 pscribd
A discrete uniform distribution is characterized by:
a. Equal probability for each value
b. Different probability for each value
c. Probability sum greater than 1
d. No fixed probability
Answer: a. Equal probability for each valuescribd
As n increases, a binomial distribution with p=0.5 approaches:
a. Poisson
b. Normal
c. Exponential
d. Uniform
Answer: b. Normaltestbook
Which distribution does NOT have memorylessness property?
a. Exponential
b. Geometric
c. Poisson
d. Binomial
Answer: d. Binomialitfeature
Which is TRUE for continuous probability distributions?
a. P(X=x)=0 for any real number x
b. Probabilities are calculated over intervals
c. Sum of probabilities can exceed 1
d. None of these
Answer: b. Probabilities are calculated over intervalsitfeature
Mean of Poisson distribution is:
a. λ
b. λ^2
c. 1/λ
d. nλ
Answer: a. λtestbook
If a distribution has right tail longer than the left, it is:
a. Symmetrical
b. Negatively skewed
c. Positively skewed
d. Uniform
Answer: c. Positively skeweditfeature
The cumulative distribution function (CDF) of a random variable X gives:
a. Probability X=x
b. Probability X≤x
c. Frequency of X
d. None of these
Answer: b. Probability X≤xtestbook
Which probability distribution is used for modeling time between events?
a. Binomial
b. Poisson
c. Exponential
d. Uniform
Answer: c. Exponentialtestbook
In normal distribution, approximately what percent of data falls within one standard deviation of the mean?
a. 68%
b. 95%
c. 99%
d. 50%
Answer: a. 68%testbook
The binomial distribution is defined for:
a. Infinite sample space
b. Only two possible outcomes
c. More than two outcomes
d. Continuous variables
Answer: b. Only two possible outcomestestbook
Which is NOT a property of probability distributions?
a. Non-negativity
b. Sum of probabilities equals 1
c. Probabilities can be negative
d. Probabilities between 0 and 1
Answer: c. Probabilities can be negativetestbook
The expected value of a uniform distribution on interval [a, b] is:
a. b
b. a
c. (a+b)/2
d. ab
Answer: c. (a+b)/2scribd
The variance of a normal distribution is:
a. σ
b. σ^2
c. μ^2
d. λ
Answer: b. σ^2testbook
Hypergeometric distribution is used for:
a. Sampling with replacement
b. Sampling without replacement
c. Continuous variables
d. Multinomial experiments
Answer: b. Sampling without replacementitfeature
Which function describes probability for discrete random variables?
a. PDF
b. PMF
c. CDF
d. None
Answer: b. PMFtestbook
The value of the probability mass function must satisfy:
a. sum = 0
b. sum = 1
c. sum < 1
d. sum > 1
Answer: b. sum = 1scribd
Which of the following is NOT a discrete distribution?
a. Binomial
b. Poisson
c. Exponential
d. Geometric
Answer: c. Exponentialitfeature
The parameter for rate in exponential distribution is commonly denoted by:
a. σ
b. λ
c. μ
d. n
Answer: b. λtestbook
The mean and variance for a Bernoulli distribution are:
a. p, p(1–p)
b. 1, 0
c. p, p^2
d. 1, p
Answer: a. p, p(1–p)itfeature
In a normal distribution, the mean, median, and mode are:
a. Equal
b. Different
c. Median > Mean
d. Mode > Median
Answer: a. Equaltestbook
Geometric distribution models:
a. Number of successes in n trials
b. Trials until first success
c. Time between events
d. Number of failures
Answer: b. Trials until first successitfeature
If the probability density function is negative at some point:
a. Valid
b. Invalid
c. Acceptable for discrete case
d. Acceptable for normal distribution
Answer: b. Invalidtestbook
The discrete random variable X has possible values:
a. Finite or countably infinite
b. Infinite only
c. Uncountable
d. Non-numeric
Answer: a. Finite or countably infinitetestbook
The cumulative probability at x for a continuous distribution is:
a. Area under PDF upto x
b. Value of PDF at x
c. Mean up to x
d. Variance at x
Answer: a. Area under PDF upto xtestbook
Which is true for a probability distribution?
a. All probabilities sum to 1
b. Some probabilities can exceed 1
c. Probabilities can be negative
d. Probabilities always zero
Answer: a. All probabilities sum to 1scribd
The binomial distribution is a special case of:
a. Poisson
b. Multinomial
c. Normal
d. Uniform
Answer: b. Multinomialscribd
Poisson distribution is suitable when:
a. Events are independent
b. Event occurs rarely
c. Fixed interval
d. All of these
Answer: d. All of thesetestbook
The exponential distribution is memoryless because:
a. Probability does not depend on past events
b. It depends only on future events
c. Memory exists
d. Averages are always zero
Answer: a. Probability does not depend on past eventsitfeature
In continuous probability distribution, probability of taking any one exact value:
a. Zero
b. One
c. Undefined
d. Infinite
Answer: a. Zeroitfeature
Mean deviation in moderately asymmetrical distribution is:
a. 1.25 times standard deviation
b. Same as standard deviation
c. Half standard deviation
d. Double standard deviation
Answer: a. 1.25 times standard deviationtestbook
Full joint probability distribution involves:
a. All random variables
b. Only one random variable
c. Only output variable
d. None
Answer: a. All random variablesdiptisurvase.wordpress
In probability distribution, randomness refers to:
a. Unpredictability of outcomes
b. Fixed outcomes
c. Deterministic values
d. Zero probability
Answer: a. Unpredictability of outcomesdiptisurvase.wordpress
Binomial probability mass function is given by:
a. (n choose x) p^x (1–p)^(n–x)
b. p^x
c. λ^x
d. x/n
Answer: a. (n choose x) p^x (1–p)^(n–x)testbook
The normal distribution is also referred as:
a. Bell-shaped curve
b. Step function
c. Linear distribution
d. U-shaped curve
Answer: a. Bell-shaped curvetestbook
For a random variable X, E[X] represents:
a. Expected value
b. Variance
c. Mode
d. Median
Answer: a. Expected valuetestbook
The probability distribution of sum of two independent normal random variables is:
a. Normal
b. Binomial
c. Uniform
d. Poisson
Answer: a. Normaltestbook

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