Flashcards in Exam 2 Deck (28)
What are two mutually Exclusive events?
Two events are mutually exclusive if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both.
What are independent Events?
When two events are said to be independent of each other, what this means is that the probability that one event occurs in no way affects the probability of the other event occurring. An example of two independent events is as follows; say you rolled a die and flipped a coin.
What are dependent events?
The outcome of choosing the first card has affected the outcome of choosing the second card, making these events dependent. Definition: Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.
What is empirical probability?
Experimental: you take the # of times an event occurred/total # of times it was preformed
What is classical probability?
Theoretical: Take the # of ways something can occur/# of simple events
what are compound events?
events composed of two or more events
When two events are mutually exclusive what is the probability that A or B will occur?
For this you just add the two events probability together because they are mutually exclusive of each other
how do you use the addition rule when two events are not mutually exclusive?
you add the probability of each event occurring and then you subtract the probability of the events happening twice. you have to subtract the probability of their intersection
How do you find the probability of independent events?
Independent events are those not affected by another event. So in order to find the proability of two INDIe events you just have to multiply them together
What is an easy way to remember dependent and independent probabilities?
Dependent probs are not the same and independent prob are always the same
how do you find probability of dependent events?
P( A and B)=P(A)*P(A give B has occurred)
What are the steps to solve conditional probability?
Find the probability of the first event and multiply the prob of the next events in line
What is a factorial?
A factorial means to muiltiply the given number by however man numbers come before it.
What is a permutation?
This means order matters
Order doesn't matter
Where does Data come from?
What is a random variable?
This is something that can assume a value for every outcome in a sample space
What is a discrete Variable?
Variables are discrete if they can be put into a list of separate items
What is a probability Distribution?
Function p(x) that assigns a probability to each outcome. This can tell us about the fixed nature of something
What is the range?
It is the largest subtracted from the smallest
What is the mean?
Mean is the average: It is the total sum of all numbers divided by the the number of values in a given set
What does Variance mean or tell you?
variance is basically a measure of the general dispersion of data in a sample, it gives you a sense of how far away data points are from one another. the larger the variance, the more variability you have in your sample (in whatever it is you are measuring).
What is and example Standard Deviation
standard deviation is more concrete: it is the average distance of each point in the sample from the sample mean in terms of the original units of measurement. for instance, say you want to estimate the average height of a high school male basketball player. you take a sample of 10 varsity basketball players from your school and calculate their height and standard deviation. say you find that the mean of the sample is 70 in with a standard deviation of 2, you can say that the average difference between any given high school varsity basketball player is 2 inches from the mean of 70. it gives you a tool for making educated predictions about a population. if your sample is normally distributed, you can make even more educated predictions; in a normal distribution, 68% of the population falls between -1 and +1 standard deviations (from the mean), 95% of the population falls between - 2 and +2 SD, and approximately 99% of the population falls between - 3 and +3.
What does a z score tell you about data and the Standard Deviation?
The z score for an item, indicates how far and in what direction, that item deviates from its distribution's mean, expressed in units of its distribution's standard deviation Z scores are sometimes called "standard scores". The z score transformation is especially useful when seeking to compare the relative standings of items from distributions with different means and/or different standard deviations.
What does it mean for something to Deviate?
depart from an established course.
What is the purpose of finding binomial distribution?
The binomial probability distribution is useful when a total of n independent trials are conducted and we want to find out the probability of r successes, where each success has probability p of occurring. There are several things stated and implied in this brief description. The definition boils down to these four conditions:
Fixed number of trials
Two different classifications
Probability of success stays the same for all trials
What is a continuous Random Variable?
A variable is continuous if it s values are on a continuous spectrum