Suppose you have n trials of an experiment in which the probability of "success" in each trial is p. Then the probability of r successes is:
nCr*pr*(1-p)n-r for r = 0, 1, ... n.
nCr = n!/[r!*(n-r)!]
discrete & continuous
Strictly speaking, there are no cons because they are defined for discrete variables only. The only con that I could think of is the difficulty evaluating the moments and other probabilities for some discrete distributions such as the negative binomial.
Two independent outcomes with constant probabilities.
Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.
If you're studying a subject involving or related to statistics and probability, then it will. If you're not, then it won't.
discrete & continuous
It is "probability".
There is no such thing. The Normal (or Gaussian) and Binomial are two distributions.
No.
Discrete
Read the instructions that accompany the table: they do not all have exactly the same layout.
Strictly speaking, there are no cons because they are defined for discrete variables only. The only con that I could think of is the difficulty evaluating the moments and other probabilities for some discrete distributions such as the negative binomial.
In a symmetric binomial distribution, the probabilities of success and failure are equal, resulting in a symmetric shape of the distribution. In a skewed binomial distribution, the probabilities of success and failure are not equal, leading to an asymmetric shape where the distribution is stretched towards one side.
There are several types of distributions in statistics, including normal, binomial, Poisson, uniform, and exponential distributions. The normal distribution is bell-shaped and commonly used due to the Central Limit Theorem. Binomial distributions deal with binary outcomes, while Poisson distributions model the number of events in a fixed interval. Uniform distributions have constant probability across a range, and exponential distributions often describe time until an event occurs.
Studying the binomial theorem is essential because it provides a powerful method for expanding expressions of the form (a + b)^n, enabling efficient calculations in algebra and combinatorics. It lays the groundwork for understanding probabilities, as it relates to binomial distributions, which model various real-world scenarios. Additionally, the theorem enhances problem-solving skills and is applicable in calculus, making it a vital concept in higher mathematics.
Well... the probabilities should add up to exactly 1 and cannot be negative.
The distribution depends on what the variable is. If the key outcome is the number on the top of the die, the distribution in multinomial (6-valued), not binomial. If the key outcome is the number of primes, composite or neither, the distribution is trinomial. If the key outcome is the number of sixes, the distribution is binomial with unequal probabilities of success and failure. If the key outcome is odd or even the distribution is binomial with equal probabilities for the two outcomes. Thus, depending on the outcome of interest the distribution may or may not be binomial and, even when it is binomial, it can have different parameters and therefore different shapes.