Sampling distribution (Rozkład próbkowania)
Distribution of statistic estimates we would see if we selected many random samples using same sampling design, and computed an estimate from each.
Central Limit Theorem: CLT (Centralne twierdzenie graniczne)
With large enough probability sample size, sampling distribution of estimates will look like a normal distribution, regardless of what estimates are being computed.
z-score
A z-score measures exactly how many standard deviations above or below the mean a data point is, assuming normal distribution.
Density Curve (Funkcja gęstości prawdopodobieństwa)
If you draw relative frequency historgram of probability distribution with very small bins, the tops will form a density curve.
Nieujemna funkcja rzeczywista, określona dla rozkładu prawdopodobieństwa, taka że całka z tej funkcji, obliczona w odpowiednich granicach, jest równa prawdopodobieństwu wystąpienia danego zdarzenia losowego
Random Variables (Zmienna losowa)
Variable whose values depend on outcomes of a random phenomenon.
Probability Distribution (Rozkład prawdopodobieństwa)
- Function P(X) = Y
- Probability distributions describe the probability of all possible outcomes of a given variable.
Expected Value (Wartość oczekiwana)
The mean of a probability distribution.
Expected value uses probability to tell us what outcomes to expect in the long run.
Coin flip example: 0.5
Probability distribution Variance
Var = (xi - E(X))^2 * P(xi) for all xi
STD = sqrt(Var)
How addition to random variable changes mean and variance? (i.e. X + k)
Sum changes variable mean (mean + k) but does NOT change standard deviation/variance.
How multiplication of k and random variable changes mean and variance? (i.e. X * k)
Multiplication changes variable mean (mean * k) AND standard deviation/variance (k * STD)
When can we combine random variables?
Make sure that the variables are independent or that it’s reasonable to assume independence, before combining variances.
Mean (m) and Variance (v) of E(X + Y)
m = mX + mY, v = vX + vY
Mean (m) and Variance (v) of E(X - Y)
m = mX - mY, v = vX + vY
standard error
the standard deviation of a sampling distribution
What is CDF function
- Cumulative Distribution Function (CDF)
- Example: the probability of our IQ (which is the random variable X) being less than or equal to 120 (i.e. P(X ≤ 120) can be determined using the CDF.
- It gives the probability of finding the random variable at a value less than or equal to a given cutoff, ie, P(X ≤ x).
What is PDF function
- Probability Density Function (PDF)
- Example: if we want the probability for a specific height x = 39
- statistical expression that defines a probability distribution (the likelihood of an outcome) for a discrete random variable
