This module contains a set of definitions from statistics that might be useful for advanced undergraduates.
Important definitions in statistics
It is not unusual for students to forget important concepts learned in an earlier course. This set of definitions is intended to stir memories of those wonderful times when you were learning statistics and econometrics. It is not intended to replace a statistics course but to provide you with a handy guide to the denfinition of some important terms in the statistical tools used by economists.
Random variables
Random experiment
A random experiment is an experiment whose outcome is uncertain.
Outcome space
The outcome space (also sometimes referred to as the sample space) is the list of all possible outcomes of a random experiment.
Single toss of a coin.
Consider the toss of a coin. Since the outcome is uncertain, tossing the coin is an example of a random experiment. The outcome space consists of a heads and a tails. If we let
X be 0 if the outcome is a heads and let
X equal 1 if the outcome is a tails, then
X is a random variable. Since
X only can take on integer values (0 or 1), it is a discrete random variable.
Random variable
A random variable is a number that can be assigned to an outcome of a random experiment. A discrete random variable has a finite number of possible values while a continuous random variable has an infinite number of potential values.
Non-stochastic variable
A non-stochastic variable is any variable that is not a random variable; i.e., does not represent the outcome of a random experiment.
Multiple tosses of a coin.
Let
x equal the number of heads that occur when a coin is tossed n times. The tossing of the coin
n times is a random experiment. The outcome space of this random experiment is an integar between 0 and
n . Since the value
x is equal represents the outcome of a random experiment, it is a random variable.
Random sample
A random sample of size
n out of a population of size
N has the characteristic that every member of the population is equally likely to be chosen.
Height of college age women.
Consider a random sample of the population of college age women. The height,
x , of any woman chosen from this population is a random variable with a value somewhere in the outcome space, where the outcome space is a number between (say) 24 and 96 inches. Since in theory we can have as accurate a measurement as we might like,
x can be thought of as being a continuous random variable.
Probability
General terms
Probability distribution for a discrete random variable.
Consider a discrete random variable
that represents an outcome of the
n potential outcomes of a random experiment—that is, the set of potential outcomes is represented by
Any function is a probability if and only if (1)
(2)
for all i and j, and (3)
An example of a discrete distribution is in Example 4.
Discrete distribution.
Figure 1 illustrates a discrete probability distribution where
goes from 1 to 8. The areas in the shaded rectangles sum to 1.
A discrete probability function
The areas of the rectangles sum to 1.
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
