What is the difference between a normal profile of a random variable and normal pdf of a random variable.

Question
Data distributions
asked 2021-03-11
What is the difference between a normal profile of a random variable and normal pdf of a random variable.

Answers (1)

2021-03-12
Step 1
From the given information,
A random variable is a function X with a particular domain and range that takes all possible outcomes from the function of the event or distribution. The random variable may be continuous or discrete in nature and any distribution function may or may not be followed.
Step 2
To explain these bell-shaped data distributions, we use a mathematical model with a smooth bell-shape curve.
These models are called regular curves or distributions that are normal. In several different types of common measurements, they were first named "normal" because the pattern occurred. This is a normal rv profile.
The normal distribution is by far the most relevant distribution of probabilities.
The Central Limit Theorem (CLT) that we will discuss later in the book is one of the key explanations for that. To give you an idea, the CLT states that the distribution of the sum would be roughly normal under some conditions if you add a large number of random variables. The meaning of this outcome is that many random variables can be expressed as the sum of a large number of rankings in real life.
Consider a random variable X. with expected value as \(\displaystyle{E}{\left({X}\right)}{\quad\text{and}\quad}{v}{a}{r}{i}{a}{n}{c}{e}{a}{s}{V}{a}{r}{\left({X}\right)}{t}{h}{e}{n}\frac{{{X}-\mu}}{\sigma}\) A normalization or normal profile of the random variable is considered. Example: It is said that Random Variable X follows the Binomial distribution.\(\displaystyle{X}\sim{B}\in{\left({n},{p}\right)}\) and we know that the binomial distribution expected value is E(X) = np and Variance, Var(X) = npq. In the form, then, random variable \(\displaystyle{X}\frac{{{X}-{n}{p}}}{{n}}{p}{q}\) has a normal profile.
A random variable X is said to follow Normal distribution then X having probability distribution function
\(\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{\sqrt{{{2}\pi\sigma}}}}{e}^{{-\frac{{1}}{{2}}{\left(\frac{{{x}-\mu}}{\sigma}\right)}^{{2}}}}{x}\in{R}\) is known as normal pdf of a random variable. where \(\displaystyle\mu{i}{s}{m}{e}{a}{n}{\quad\text{and}\quad}\sigma\) is standard deviation of the normal distribution.
0

Relevant Questions

asked 2021-02-09
What is the difference between a normal profile of a random variable and normal pdf of a random variable. What is the median value of a random variable having a normal pdf.
asked 2020-12-09
There're 5.2 liters of blood in an average person's system. Assume, that the variable is normally distributed. The standard deviation is 0.3. What is the percentage of people with less than 5.4 liters in their system?
asked 2020-12-24
According to Census data, 1950 the population of the U.S amounted to 151.3 million persons, and 13.4% of them were living in the West. In 2000, the population was 281.4 million, and 22.5% of them were living in the West. Is the difference in percentages practically significant? statistically significant? Or do these questions makes sense? Explain briefly.
asked 2020-11-26
We have a data set (n=100) with hormone concentrations and the frequency of each value. Assuming normal (continuous) distributions, We need to determine the parameters of the continuous probability distribution functions.
asked 2021-03-01
A yoga class consists of 90 males and 110 females. What is the ratio of male to female students?
asked 2020-11-08
What is a frequency distribution of qualitative data and why is it useful?
asked 2021-02-25
5 building's height's \(\displaystyle\mu={56}\) m. Three of them are 58m, 55m and 53m. What is the mu for the 2 remaining buildings?
asked 2021-01-07
What do the mean deviation, variance and standard deviation all have in common? How is this common factor (s) helpful with the calculations of the mean deviation, variance and standard deviation?
asked 2020-11-10
A sample is taken (21, 19, 11, 18, 18).
1. How big is the original data set?
2. What percentege of data is 11?
asked 2021-01-22
A county is populated with 20,899,000 people, while the population is growing at a rate of 3.2% per year. What will the population be in 19 years? Round the answer to the nearest thousand.
...