I need help when solving these kind of problems: -Exponential distribution -Norm

Question

I need help when solving these kind of problems:

-Exponential distribution

-Normal distribution

-Binomial distribution

-Poission

-Y=min(4,X) or Y=max(5,X)

-Uniform distribution with var(x)=5

What should I be looking for in order to solve them? Are there specific formulas for each of them that whenever a problem presents itself with (example: exponential distribution) that I can just use this formula and insert whatever is given from the problem to then find a solution? Are there any words that can give me clues to which distribution should be used?

*I really need help with this. Once I know what the problem is asking, it will be so much easier to then solve whatever test question is presented to me. Thank you*

Explanation / Answer

Let us start understanding with Binomial distribution

.

Binomial distribution is used when there is a discrete distribution of the variable . there are only two outcomes and fixed trials.

Examples:

Outcome of exam: two outcomes: pass or fail

Tossing a coin : head or tail

Rain: rain or no rain

like this every event can have two possible outcomes

when such experiment is repaeated for limited number of trials and each trial is independent of th other , we make use of Binomial probability

.

Poisson distribution: This is special case of Binomial distribution only

In this case: the probability of success is very small (p tends to 0) and number of trials is very large (n tends to infinity)

Example: Number of defects in a page

Number of accidents on roads

Number of defects in production of bulbs

A simple indication of poisson is when the question states the mean like: per day , per unit time , per page and so on.

.

Exponential probability: this is used to measure time between two events that follow poisson distribution

Thus it is related to poisson , and it deals with time directly

.

Normal distribution: this is used for variables that are continuous, for example: height of people can be expressed in decimals as well , Weight of people and so on

In questions that deal with normal distribution , they will specifically provide you Mean and standard deviation for sure

So this will help understand that the question relates to normal distribution

.

Uniform distribution will specify the range [a,b] and state that it is uniformly distributed

it is a type of continuous distribution only, the only difference is that in it all the values are equally likely

that is why it has rectangular shape

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