Module 5 Flashcards
What is a random trial?
A random trial is any process with multiple outcomes where the result of any specific trial is unknown. For example, flipping a coin is a random trial because the outcome (heads or tails) is not known until the coin lands.
What is the sample space in a random trial
The sample space is the set of all possible outcomes of a random trial. It is typically written in curly braces. For example, the sample space for a coin flip is {heads, tails}.
How is probability defined according to the frequentist approach?
Frequentist probability is defined as the proportion of times an event occurs if a random trial is repeated many times. For example, the probability of rolling a 1 on a fair six-sided die is 1/6 because, over thousands of rolls, 1 will come up about one-sixth of the time.
What does the Law of Large Numbers state?
The Law of Large Numbers states that as a random trial is repeated many times, the observed frequency of an event gets closer to the theoretical probability of that event. For example, flipping a fair coin many times will result in the proportion of heads being close to 0.5.
What is a random variable, and how does it differ from a sample variable?
- A random variable is a variable that takes on values based on the outcomes of a random trial. It can be discrete or continuous.
- A sample variable, in contrast, is a specific value observed from a sample. For example, if X is the random variable representing the outcome of rolling a die, then a sample variable could be X = 4 from one roll.
What is the difference between discrete and continuous random variables?
Discrete random variables take on specific, countable outcomes, such as the number of heads in coin flips. Continuous random variables take on any value within a range, such as the time it takes for a train to arrive.
What is probability distribution
Describes the likelihood of different outcomes for a random variable. It shows how probabilities are distributed across the range of possible outcomes. The area under the probability distribution sums to 1.
Discrete Probability Distribution
characterized by a series of bars representing probabilities for each possible outcome of a discrete random variable.
- For example, rolling a six-sided die has probabilities represented for each outcome (1, 2, 3, 4, 5, 6).
What characterizes a continuous probability distribution?
Represented by a smooth curve where the area under the curve over a specific range indicates the probability of outcomes within that range.
For example, a normal distribution is a continuous probability distribution.
What is a standard Normal distribution?
Normal distribution is a mean of 0 and a standard deviation of 1. It is used to standardize data for comparison and to find probabilities using z-scores.
How do you calculate a z-score?
A z-score is calculated using the formula: z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation. It indicates how many standard deviations a value is from the mean.
