Free Probability Distributions MCQs with Answers

• A. Positively skewed
• B. Negative skwed
• C. Symmeteric
• D. No shape

Explanation: When p equals q, the probabilities of success and failure are balanced, so the binomial distribution is symmetric around its mean.

• A. Positively skewed
• B. Negatively skewed
• C. Symmetric
• D. Bell shapedMaster Coding Skills

Explanation: For a binomial distribution, skewness has the sign of q minus p. Here q is 0.4 and p is 0.6, so q minus p is negative and the distribution…

• A. Gamma distribution
• B. Binomial distribution
• C. Negative binomial dis
• D. Possion distribution Mathematics

Explanation: The number of events or successes occurring in a fixed time interval under a constant average rate follows the Poisson distribution.

• A. Possion distribution
• B. Exponential distribution
• C. Gamma distribution
• D. Beta distribution

Explanation: The time between successive successes in a Poisson process follows an exponential distribution because it models the waiting time for the…

• A. From larger values of x
• B. From smallest upto specific value of x
• C. From zero to specific value of x
• D. None of theseMarketing

Explanation: The cumulative distribution function is F(x) = P(X ≤ x), so it accumulates probability from the smallest possible values up to the…

• A. Variable
• B. Probability distribution
• C. Values
• D. None of these

Explanation: A random variable is defined together with a probability distribution that describes how likely its possible values are.

• A. None
• B. X-axis
• C. Y-axis
• D. Along Y=X

Explanation: The normal curve approaches the horizontal axis indefinitely but never actually touches it, so it is asymptotic to the X-axis.

• A. have no Mode
• B. Multi Modal
• C. Bi Modal
• D. Tri Modal
• E. Uni Modal

Explanation: A normal distribution has one peak at its mean, median, and mode, so it is unimodal.

• A. β1=β4
• B. Mean=Mode=Median
• C. µ1=µ4
• D. µ1=µ2

Explanation: For the standard symmetric, unimodal distribution, the center is the same by all three measures: mean = median = mode.

• A. 49
• B. 16
• C. 7
• D. 4

Explanation: In the notation X ~ N(16, 49), the first parameter is the mean and the second is usually the variance.

• A. 135
• B. 50
• C. 70
• D. 60

Explanation: For a linear transformation, E(Y) = 5E(X) + 10. Substituting E(X) = 10 gives E(Y) = 5(10) + 10 = 60.

• A. 1
• B. Mean value
• C. 0.5
• D. 2
• E. -1

Explanation: The normal curve is symmetric about its mean, so the total area is divided equally between the two sides.

• A. None
• B. Mode
• C. Standard Deviation
• D. Mean

Explanation: The standard deviation controls the spread of a normal curve: a larger value makes it wider and flatter, while a smaller value makes it…

• A. None
• B. Mean
• C. Quartile
• D. Standard Deviation
• E. Mean Deviation

Explanation: For a normal distribution, the standard deviation determines the curve's spread and therefore its shape or flatness.

• A. 1
• B. 0.5
• C. 0.3989
• D. None of these

Explanation: The standard normal density is highest at its centre, Z = 0, where its ordinate is 1 divided by √(2π), approximately 0.3989.

• A. 0.5
• B. 1
• C. 2
• D. 3

Explanation: A normal distribution has zero skewness, so β1 = 0. Its moment coefficient of kurtosis is β2 = 3, which is the mesokurtic benchmark.

• A. β1
• B. µ2
• C. β2
• D. µ3

Explanation: The third central moment, μ3, carries the direction of skewness: it is positive for right skewness and negative for left skewness.

• A. 100
• B. 1
• C. 50%
• D. 1%

Explanation: The total probability represented by a continuous probability distribution is 1, so the entire area under the normal curve is 1, or 100%.

• A. Symmetrical
• B. non-symmetrical
• C. + vely skewed
• D. -vely skewed

Explanation: The normal curve is symmetric about its mean, with equal left and right halves and zero skewness.

• A. Zero
• B. Negative
• C. Positive
• D. None of these

Explanation: Because z = 0 is the centre of the standard normal curve, values to its right are positive z-values.