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Are all symmetric distributions normal distributions?
No. There are many other distributions, including discrete ones, that are symmetrical.
Why can a function not be a probability mass function?
A function cannot be a probability mass function (PMF) if it violates the properties of a PMF. A PMF must assign a non-negative probability to each possible outcome of a discrete random variable, and the sum of probabilities for all possible outcomes must be equal to 1. If a function does not satisfy these properties, it cannot be considered a PMF.
What is the probability of winning the lottery depends on how many tickets you buy?
It is a true statement. If you buy them all, the probability of your winning is 1!It is a true statement. If you buy them all, the probability of your winning is 1!It is a true statement. If you buy them all, the probability of your winning is 1!It is a true statement. If you buy them all, the probability of your winning is 1!
What is difference between proportion and probability?
Proportion is the probability of a selected sample. probability is the true probability of all cases. If this is not what you are looking for then please specify.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
How do you find the mean of frequency distributions?
For discrete distributions, suppose the variable X takes the specific value x with probability P(X=x) Then add together x * P(X = x) for all possible values of x. For continuous distributions, suppose the probability distribution function of the variable X is f(x). Then the mean is the integral of x*f(x) with respect to x, taken over all possible values of x.
How do calculate the probability of at most?
For a discrete variable, you add together the probabilities of all values of the random variable less than or equal to the specified number. For a continuous variable it the integral of the probability distribution function up to the specified value. Often these values may be calculated or tabulated as cumulative probability distributions.
Are all symmetric distributions normal distributions?
No. There are many other distributions, including discrete ones, that are symmetrical.
Can you use this less than 5 percent rule for all normal probability distributions?
The answer depends on what "this less than 5 percent rule" is, in contrast to some other 5 percent rule!
Why can a function not be a probability mass function?
A function cannot be a probability mass function (PMF) if it violates the properties of a PMF. A PMF must assign a non-negative probability to each possible outcome of a discrete random variable, and the sum of probabilities for all possible outcomes must be equal to 1. If a function does not satisfy these properties, it cannot be considered a PMF.
A complete probability distribution is always an objective listing of all possible events Since it is impossible to list all the possible outcomes from a single event probability distributions are o?
Your question is not clear, but I will attempt to interpret it as best I can. When you first learn about probability, you are taught to list out the possible outcomes. If all outcomes are equally probable, then the probability is easy to calculate. Probability distributions are functions which provide probabilities of events or outcomes. A probability distribution may be discrete or continuous. The range of both must cover all possible outcomes. In the discrete distribution, the sum of probabilities must add to 1 and in the continuous distribtion, the area under the curve must sum to 1. In both the discrete and continuous distributions, a range (or domain) can be described without a listing of all possible outcomes. For example, the domain of the normal distribution (a continuous distribution is minus infinity to positive infinity. The domain for the Poisson distribution (a discrete distribution) is 0 to infinity. You will learn in math that certain series can have infinite number of terms, yet have finite results. Thus, a probability distribution can have an infinite number of events and sum to 1. For a continuous distribution, the probability of an event are stated as a range, for example, the probability of a phone call is between 4 to 10 minutes is 10% or probability of a phone call greater than 10 minutes is 60%, rather than as a single event.
Sampling error concerns natural variation between samples is always present and can be described using probability Is this true?
No, it is not true. Probability can be used to describe some properties of the variation but not all.
What is the basic principle behind quantum mechanics?
The theory of quantum mechanics is mostly based on the idea that all particles are describe by wave functions. In other words, particles are not simply items located at a specific point in space. Instead they can only be described by probability distributions, we can only say that a particle has some probability of being found at some point in space, and that the particles may be found ANYWHERE in the universe (though with varying probability).The basic principles of quantum theory are Schrodinger's equation (which describes the evolution of a particle's probability amplitude with time), Heisenberg's uncertainty principle, (which denies the ability of science to ascribe a definite trajectory of a particle), and in some texts, the "canonical commutation relation" is presented as a fundamental principle of QM.
Normal distribution is symmetric with single peak.Does this mean that all distibutions are normal?
No, not all distributions are symmetrical, and not all distributions have a single peak.
Is the sum of deviations from the mean equal to zero in symmetrical distributions?
It is equal to zero in ALL distributions.
Why are electrons different sizes?
Electrons are considered point particles in the Standard Model of particle physics, meaning they are considered to have no size. However, they exhibit properties like mass and charge that give them characteristics of a physical object. Their behavior is described by quantum mechanics, where they are represented as probability distributions rather than localized particles.
What is lambda in statistics?
Lamdba (like most Greek letters in statistics) usually denotes a parameter of a distribution (usually of Poisson, gamma or exponential distributions). This will specify the entire distribution and allow for numerical analysis of the probability generating, moment generating, probability density/mass, distribution and/or cumulant functions (along with all moments), as and where these are defined.
