Basic Statistical Concepts

Random Variable

• Random variable: A random variable is a rule that assigns a numerical value to each outcome in a sample space. Random variables may be either discrete or continuous. For example:

  • Discrete Random variable: The number of heads when flip a coin 10 times.

  • Continuous Random variable: The time a student to finish the test,

• Mean,std,

  • Mean of random variable: If X is the random variable and P(X=x) is the respective probabilities, the mean of a random variable is defined by:

  • Mean (μ) = ∑ xP(X=x)

  • where variable X consists of all possible values and P consist of respective probabilities.

  • Variance of Random Variable: The variance tells how much is the spread of random variable X around the mean value. The formula for the variance of a random variable is given by;

    • Var(X) = σ² = E(X²) – [E(X)]² where E(X²) = ∑x²P(X=x) and E(X) = ∑ xP(X=x)

  • Standard deviation std(X)= Sqrt(Var(X))

• Average, sample std

• Median, Quantile, percentile

• Skewness: Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or normal distribution. If the curve is shifted to the left or to the right, it is said to be skewed.

Hypothesis testing concepts

• Hypothesis

• Statistics

• p_value, typeI error, type II error

Model selection criterial