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 is negatively skewed.

• 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. The binomial distribution instead counts successes in a fixed number of independent trials.

• 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 next event. The gamma distribution applies to the waiting time until the second or later event.

• 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 specified value x. This distinguishes it from a probability mass or density function at one value.

• 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. Merely having numerical values does not distinguish a random variable from an ordinary variable.

• 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. The Y-axis only passes through the curve's center when the distribution is centered at zero.

• 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. Bi-modal and multi-modal distributions have two or more peaks.

• 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. Symmetry also makes the odd central moments zero, but that relationship is not represented correctly by the other options.

• 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. Therefore, the mean is 16, while 49 is the variance and 7 would be its standard deviation.