Probability Distribution

Continuous Distribution 🚙

The continuous Distribution follows

Normal Distribution

Student T Distribution

Logistic Distribution

Exponential Distribution

Normal Distribution:

• The normal distribution can be denoted by N(μ,σ²) The normal distribution occurs in nature as well as in various shape and forms.

Normal Distribution

• Graph of the normal distribution is bell-shaped and symmetric.

Photo by kabita Darlami on Unsplash

• In the normal distribution, outliers are very rare.
• The expected value for normal distribution:

Standardizing Normal Distribution: before This, we need to know what is transformation?

• Transformation A way we can alert every element of distribution to obtain a ‘new distribution’.
• Standard is a special kind of transformation.
• To perform, move the graph left or right until μ=0

Student's t distribution

This distribution is defined by t(K) where K represent — degrees of freedom. Student’s T distribution is a small sample size approximation of a normal distribution.

• Student’s T distribution is also called T-distribution.
• We can easily identify student’s T distribution where the Graph of the distribution is also bell-shaped and symmetric, with fatter tails.

• To calculate the central tendency of mean we use the formula

Mean: E(y)=μ

• It is used for statistical analysis.
• This distribution is widely used for hypothesis testing with limited data.

Chi-square distribution

This distribution can be denoted by a capital Greek letter χ2 (K)and used for statistical analysis like Hypothesis testing, computing intervals, test for goodness of fit in categorical values.

• Graph for Chi-square distribution is non-symmetric.

• Expected value:

E(X)=K

Var(X)=2K

Exponential distribution:

It can be denoted by Exp(λ)

• Eg: youtube views.
• Graph of distribution is like a boomerang.

Logistic Distribution:

• Denoted by logistic (μ, S)
• Where μ is the mean(location) and S — Scale parameter

Probability in Finance:

• Example option pricing: Choosing premium which cost 100rs but profits 900rs, whereas the non-premium offers 100rs but only prediction not
• Non-premium: No guarantee is gain(invert)1000+or else you will lose 1000rs.

E(P)<0(Bad deal)

E(P)=0(Far deal)

E(P)>0(Good deal)

Probability in statistics:

Statistics: Focus on samples and incomplete data to analyze numeric and categorical data.

Hypothesis testing:

Generally, a hypothesis means an idea that can be tested Eg: Choose a dress and take it out for trial.

• Have to know what type of distribution is our sample.
• After knowing we can create a different model (Regression), This process is called mathematical modelling (statistician).
• A data scientist calls this model supervised machine learning.

Probability in data science:

Monte Carlo simulation:

• The power we produce artificial data to test our mathematical model.
• It is not totally random data.
• Have the same set of conditions.

Example:- If p(x) = 0.8, then this outcome must match our mathematical model.

What is Data Science?

Data Science is an expansion of probability, statistics and programming to implement computation technology to solve advanced questions but not complete certainty.

Thank You… 😍

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Discrete Distribution 🌱

How probability distribution related to data science