Lernkarten

Karten 44 Karten 1 Lernende English Universität 08.10.2017 / 29.10.2017 Keine Angabe
3 Exakte Antworten 27 Text Antworten 14 Multiple Choice Antworten

What are random variables and probability distributions?

Random variables and probability distributions:

• X --> A random variable is a numerical measure of the outcome from a probability experiment, so its value is determined by chance. Typically, denoted as the letter, X.e.g. rolling a dice
• A probability distribution is a table, formula, or graph that describes the values of a random variable and the probability associated with these values.

What are the different probability distributions?

• Discrete variables produce outcomes that come from a counting process (e.g. number of classes you are taking)
• Continuous variables produce outcomes that come from a measurement (e.g. your annual salary, or your weight).

How can we calculate the probability that X equals a certain value in a continuous distribution?

• In continuous distributions, the probability that X equals to a certain value is zero à Because there is no area.

What is a uniform distribution?

• The uniform distribution is a probability distribution that has equal probabilities for all possible outcomes of the random variable.
• Also called a rectangular distribution

density function => 1/(b-a)

How can we calculate the probability in a uniform distribution?

bild

What is normal distribution and what is the probability of mean +- 1 sd, 2 sd and 3 sd?

• Bell Shaped, Symmetrical, Mean = Median = Mode
• Location is determined by the mean, μ
• Spread is determined by the standard deviation, σ
• The random variable has an infinite theoretical range
• μ ± 1σ encloses about 68% of X’s
• μ ± 2σ covers about 95% of X’s
• μ ± 3σ covers about 99.73% of X’s

What is the student t distribution? What are degrees of freedom?

Idea: Number of observations that are free to vary after sample mean has been calculated. It increases variation and therefore also standard deviation extremely when n is small and approximates n when n is getting bigger.

What are discrete probability distribution and what are the rules?

Recap: Discrete variables à Variables producing outcomes that come from a counting process.

Rules:

1. A fixed number of observations, n
1. e.g. 15 tosses of a coin
2. e.g. 10 light bulbs taken from a warehouse
2. Constant probability for the event of interest occurring (π) for each observation
1. e.g. Probability of getting a tail is the same each time we toss the coin.
3. Each observation is categorized as to whether the “event of interest” occurred or not.
1. e.g. head or tail in each toss of a coin
2. e.g. defective or not defective light bulb
3. When the probability of the event of interest is represented as π, then the probability of the event of interest not occurring is 1 – π.
4. Observations are independent
1. The outcome of one observation does not affect the outcome of the other

negatively skewed (LS) when p > 0,5; Symmetric when n = 10 and p = 0,5 and prositively skewed (RS) when p < 0,5

Mean = np

Var = np(1-p)

Sd = sqrt(var)