What is the explanation of probability distributions regarding the question of probability distribut

8.Let the food purchase event be A, and the other purchase event be B

p(a)=; p(b)=

p(ab)=

The first question is to ask.

p(b|a) = p(ab) p(a) = 7 16 The second question is to seek.

p(a|b)=p(ab)/p(b)=

9.Let the Know the Correct Answer event be A and the correct answer event be B

P(a)=1 2

p(b|!a)=1/4

Obviously, knowing the right answer will definitely be able to answer correctly.

So p(b|a)=1

p(!a)=1-p(a)=1/2

Thus it is obtained by the Bayes formula.

p(a|b)=p(b|a)p(a)/[p(b|a)p(a)+p(b|!a)p(!a)]

1) Because the number of failures is independent of each other, and all occurrences are possible.

i.e., a=2) exactly two failures probability p(x=2)=

3) The probability of more than one failure.

p=p(x=2)+p(x=3)=

4) The probability of a maximum failure is .

p=p（x=1）+p（x=0）=

8.A: Come to buy other goods B: Customers come to the supermarket to buy food.

1）p(a 1 b)=p(ab)/p(b)=2) p(b 1 a)=p(ab)/p(a)=10.(1) a=

8) 45% for only buying food, 25% for other goods, and 30% for the rest of the case is the probability of buying food and other goods.

Probability distributionsThe explanation is:Probability theoryOne of the basic concepts of caution is used to express itRandom variablesThe probability law of the value. The probability of an event indicates the likelihood that an outcome will occur late in an experiment. To fully understand an experiment, you must know the full range of possible outcomes of the experiment.

The probability of an event indicates how likely it is that an outcome will occur in an experiment. In order to fully understand the aspective test of the wide test rock, it is necessary to know all the possible outcomes of the test and the probability of the occurrence of various possible outcomes, i.e., the probability distribution of the random trial.

If the results of the experiment are expressed by the value of variable x, then the probability distribution of the random trial is the probability distribution of the random variable, that is, the possible value of the random variable and the probability of obtaining the corresponding value. Depending on the type of random variable to which it belongs, the probability distribution takes different forms.

Probability distribution, also known as probability distribution law, means that the probability distribution law can represent the probability of all possible outcomes of a random variable.

Then there are generally two kinds, one is continuous variables.

One is the discrete variable, of course, the two variables are not the same research problems, we find the probability distribution of the probability of the random variable to get a discrete value, and the continuous probability distribution is to get the probability of the variable in a certain region.

1.Continuous random variables.

If all the possible values of the random variable x cannot be enumerated one by one, the random variable at any point in a certain interval on the number line.

2.Discrete random variables.

Let x be a random variable, and if all its possible values are finite or infinite, then x is said to be a discrete random variable.

Classical probability, also known as ex-ante probability, refers to the fact that when the various possible outcomes in a random event and the number of occurrences can be known by deduction or extrapolation, the probability of various possible outcomes can be calculated without any statistical experiments.

Conditional probability refers to the probability of event A occurring under the condition that another event B has already occurred. The conditional probability is expressed as: p(a|b), which is read as "the probability of a under the condition of b".

In probability theory and statistics, expected value (or mathematical expectation, or mean, also known as expectation, or expectation) is the probability of each possible outcome in an experiment of discrete random variables multiplied by the sum of its outcomes.

In probability theory and statistics, a binomial distribution is n independent discrete probability distributions of the number of successes in a non-trial, where the probability of success in each trial is p. Such a single success or failure test is also called the Bernoulli test. In fact, when n = 1, the binomial distribution is the Bernoulli distribution.

The binomial distribution is the basis for the binomial experiment of significant differences.

Bernoulli distribution is also known as "zero-one distribution" and "two-point distribution". The random variable x is said to have a Bernoulli distribution, and the parameter is p (0 0 is a parameter of the distribution, which is often called the rate parameter. That is, the number of times the event occurs per unit of time.

The interval of the exponential distribution is [0, ) and if a random variable x is exponentially distributed, you can write: x exponential( ).

Probability density function:

Skewed distribution refers to the distribution of frequency distribution in which the peak of the limb is located on one side and the tail extends to the other side. It is divided into positive skewed and negatively skewed. The data with skewed distribution can sometimes be converted into a normal distribution after taking the logarithm, and the median is often used to reflect the concentrated trend of the skewed distribution.

In probability theory, a beta distribution, also known as a b distribution, refers to a set of continuous probability distributions defined in the interval (0,1) with two parameters, 0.

Probability density function:

The Weibull distribution is the theoretical basis for reliability analysis and life testing.

Probability density function:

Chi-square distribution is a type of probability distribution commonly used in probability theory and statistics. The sum of squares of k independent standard normally distributed variables obeys a chi-square distribution with degrees of freedom k. Chi-square distribution is a special gamma distribution that is one of the most widely used probability distributions in statistical inference, such as hypothesis testing and the calculation of confidence intervals.

Mathematical Definition: Probability Density Function:

There are two types of probability distributions: discrete probability distributions and continuous probability distributions. Discrete probability distributions are also known as probabilistic mass functions.

Examples of discrete probability distributions are Bernoulli distributions, binomial distributions, Poisson distributions, and geometric distributions, among others.

Continuous probability distributions, also known as probability density functions, are functions that have a continuous value, such as the value on a solid line. Normal distribution, exponential distribution, and beta distribution are all continuous probability distributions.

pdf: Probability Density Function, In mathematics, the probability density function of a continuous random variable (which can be shortened to a density function when it is not confusing) is a function that describes the probability of the output value of the random variable near a certain value point. It is not a probability per se, but a probability after the value is integrated.

PMF: Probability Mass Function, In probability theory, the probability mass function is the probability of a discrete random variable at a specific value.

CDF: Cumulative Distribution Function, also known as Distribution Function, is an integral of the probability density function, which can fully describe the probability distribution of a real random variable x. is the integration of the PDF over a specific interval.

CDF is the integral of PDF, and PDF is the derivative of CDF.

Describes the probability of an event occurring. Any CDF, which is an unsubtracted function, is ultimately equal to 1.