Distributions

Question 1

Sampling distribution (Rozkład próbkowania)

Answer 1

Distribution of statistic estimates we would see if we selected many random samples using same sampling design, and computed an estimate from each.

Question 2

Central Limit Theorem: CLT (Centralne twierdzenie graniczne)

Answer 2

With large enough probability sample size, sampling distribution of estimates will look like a normal distribution, regardless of what estimates are being computed.

Question 3

z-score

Answer 3

A z-score measures exactly how many standard deviations above or below the mean a data point is, assuming normal distribution.

Question 4

Density Curve (Funkcja gęstości prawdopodobieństwa)

Answer 4

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

Question 5

Random Variables (Zmienna losowa)

Answer 5

Variable whose values depend on outcomes of a random phenomenon.

Question 6

Probability Distribution (Rozkład prawdopodobieństwa)

Answer 6

• Function P(X) = Y
• Probability distributions describe the probability of all possible outcomes of a given variable.

Question 7

Expected Value (Wartość oczekiwana)

Answer 7

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

Question 8

Probability distribution Variance

Answer 8

Var = (xi - E(X))^2 * P(xi) for all xi

STD = sqrt(Var)

Question 9

How addition to random variable changes mean and variance? (i.e. X + k)

Answer 9

Sum changes variable mean (mean + k) but does NOT change standard deviation/variance.

Question 10

How multiplication of k and random variable changes mean and variance? (i.e. X * k)

Answer 10

Multiplication changes variable mean (mean * k) AND standard deviation/variance (k * STD)

Question 11

When can we combine random variables?

Answer 11

Make sure that the variables are independent or that it’s reasonable to assume independence, before combining variances.

Question 12

Mean (m) and Variance (v) of E(X + Y)

Answer 12

m = mX + mY, v = vX + vY

Question 13

Mean (m) and Variance (v) of E(X - Y)

Answer 13

m = mX - mY, v = vX + vY

Question 14

standard error

Answer 14

the standard deviation of a sampling distribution

Question 15

What is CDF function

Answer 15

• 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).

Question 16

What is PDF function

Answer 16

• 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