Random Variable, Probability & Probability Distribution

1. What is a Random Variable?

   The values which vary without following any pattern, that is they change randomly.

   For example, if any experiment (flipping of a coin, or rolling of a die) has the outcome bounded to be from a given set of values, and is not fixed, the result will change every time the experiment is conducted. Such an outcome is termed as Random Variable.

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2. What is the formula for Probability?

   Probability can be explained as the chance that an outcome has from a set of possible outcomes of an experiment. It is measured as = No. of interested events/Total no. of events.

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3. What are the properties of Probability?

   Probability is the ratio of the number of chances for a desired output over the total number of outputs. It will lie always between 0 and 1.

   Probability value close to 1 means the event is likely to occur and Probability close to 0 means that event is not likely to occur. Also, the sum of all the Probability values for all the possible outcomes will be equal to 1.

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4. What does Conditional Probability mean?

   Conditional Probability: The Probability of an event B (second event) given that event A (first event) which effects the event B has already occurred.

   P(A|B) = P(A&B)| P(B)

   It is the probability measured between 2 dependent events.

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5. What is Excepted value?

   The Expected value is the average outcome for an experiment conducted infinite times with each outcome having different chances.

   It is also known as the Mean of distribution (or) Average of values when the distribution is given, or weighted average.

   It is calculated as ∑ [X*P(X)]

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6. What does Probability Distribution mean?

   The possible outcomes of an experiment have varied chances. Understanding this distribution of chances/probabilities among the possible outcomes is known as Probability Distribution.

   Visualizing the distribution by plotting the data on X-axis and respective probabilities on Y-axis will allow to infer the better business conditions.

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7. Describe the types of Probability Distributions?

   Probability is calculated for the possible outcomes of an experiment. Data can be classified as Discrete and Continuous. The probability distribution is broadly classified into two types based on the type of Data that we are working with.

   Continuous probability distribution and Discrete probability distribution are two types of techniques.

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8. Explain Continuous Probability Distribution?

   The probabilities associated with Continuous Data is analyzed to infer details on the business conditions.

   The visualization of Continuous probability distribution shows a Bell curve.

   Properties to understand Continuous probability distribution are:

   • Continuous random variable ranges from -infinite to +infinite
   • Probabilities for a single value will be 0 (prob = 1/infinite)
   • Sum of all the Probabilities = 1 = Area under the Bell curve

   Under normal conditions, the Continuous data is assumed to follow these properties. Hence, the name Normal Probability Distribution.

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9. List out a few examples of Discrete Probability Distribution?

   • The Bernoulli Distribution
   • The Binomial Distribution
   • The Geometric Distribution
   • The Hypergeometric Distribution
   • The Multinomial Distribution
   • The Poisson Distribution
   • The Negative Binomial Distribution
   • Discrete uniform distribution

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10. List out a few examples of Continuous Probability Distribution?

    • Normal Distribution
    • Chi-Square Distribution
    • Fishers F Distribution
    • Students t Distribution
    • The Gamma Distribution
    • The Exponential Distribution
    • The Beta Distribution
    • The Weibull Distribution

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