What Do You Know About Bulgarian Solitaire?

Explanation
Martin Gardner developed the Bulgarian solitaire card game.

Explanation
When the total number of cards is not triangular, it means that the number of cards cannot form a triangular shape. A triangular number is a number that can be represented in the form of a triangle, where the rows of the triangle represent the number of cards in each row. Therefore, if the total number of cards is not triangular, it suggests that there is a limit or boundary that is reached, hence the term "Limit" is the correct answer.

Explanation
A Markov Chain is a gathering of arbitrary factors that depicts a progression of conceivable occasions in which the likelihood of each occasion relies just upon the past occasion. In other words, the probability of transitioning from one state to another in a Markov Chain is determined solely by the current state and not influenced by any previous states. Therefore, a Markov Chain is the correct answer as it fits the description of a gathering of arbitrary factors where the probability of each event depends only on the state achieved in the past event.

Explanation
The correct answer is "Discrete index set." In the context of representing time, a discrete index set is commonly used. This means that time is divided into distinct and separate intervals, such as hours, days, or seconds. Each interval is represented by a specific index, allowing for easy measurement and comparison of time. Other options, such as discrete state space, absolute index space, or limit state set, do not specifically relate to the representation of time.

Explanation
The mode in a triangular distribution is represented by the letter 'c'. The triangular distribution is a continuous probability distribution that is shaped like a triangle. It is defined by three parameters: a minimum value 'a', a maximum value 'b', and a mode value 'c'. The mode represents the most frequently occurring value in the distribution, or the peak of the triangle.

Explanation
A distribution is simplified when the mode, which is the value that appears most frequently in a set of data, is equal to the lower limit. This means that there is only one value that occurs most frequently and there is no variability in the data. It indicates that the data is highly concentrated around a single value, making it easier to analyze and interpret.

Explanation
The peak in a symmetric triangular distribution refers to the mode, which is the value that occurs most frequently in the distribution. This is the point of highest density or concentration of data. The mode represents the most common or typical value in the distribution.

Explanation
The mode is the value that appears most frequently in a set of data. In this case, since the upper limit is 0 and the lower limit is 1, there are no values between 0 and 1. Therefore, there is no mode in this set of data.

Explanation
The letter "a" is used to represent the lower limit.