STA 119 Lecture Notes - Lecture 7: Probability Distribution, Probability Mass Function, Random Variable

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olivejackal433

25 Sep 2016

School

University at Buffalo

Department

Biostatistics

Course

STA 119

Professor

Kuhlmann Dietrich

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A variable is a quantity that can vary. A company makes widgets and sells them for each. They can make as many widgets as they want. The number of widgets is therefore not a fixed number but a variable chosen by the company. Thus, we would want to use a variable (say x) to represent the number of widgets made. The revenue generated by these widgets is also a variable (say y) that is dependent on the number of widgets that we make. All of these quantities are variables since they can take on many possible values. The length of time it takes a person to run a mile tomorrow. The number of spots we will see after a die is rolled. How many baskets you will make when shooting 10 shots. The number of customers that will come to our restaurant tomorrow for lunch. How long it takes for an individual to get over an illness.

Related Questions

Lab Topic 1: The Process of Science

Introduction

1. Which of the following questions would you consider appropriate scientific questions that can be tested using the scientific method? For the statements that can be tested using the scientific method, explain how your experiment would be set up. Explain the different steps in the scientific method as they relate to this statement.

a. Does the pH of the soil affect the color of hydrangea flowers?

b. What properties of the soil influence the color of hydrangea flowers?

c. Do hydrangeas look more beautiful when grown in the right soil?

d. Was The Day After Tomorrow a better movie than Terminator?

e. Does grass require fertilizer in order to grow?

2. Read this hypothesis and answer the questions below:

Plants kept closer to windows grow larger than plants kept several feet away from windows.

a. Indicate the dependent variable:

b. Indicate the independent variable:

c. List 3 other variables that must be kept constant in this experiment (the control variables).

d. Write a prediction based on the above hypothesis.

Exercise 1.1

Take a Deep Breath

Students will need to take a picture of themselves or their group walking up and down on the step or doing other exercise. Include a note with your name and date on an index card in the picture. Insert picture here:

1. Identify the following in the experimental design. You will need to refer to the protocol to answer this question.

a. Independent variable:

b. Dependent variable:

c. Experimental dataset:

d. Control dataset:

e. Hypothesis:

2. Fill in the data for each individual in your group for the Breath experiment.

	Length of time breath can be held (seconds)
Individual Tested	Resting	After 1 minutes of exercise	After 5 minutes of exercise




Average (take the average for each column)

3. Look at the averages for all individuals in your group. Was the hypothesis you stated in the previous question supported by the âaverage dataâ? Explain your answer!!!

4. Now look at the data for each individual separately. Was there data for anyone in your group that did not support the hypothesis? If yes, explain whythis could be.

5. How many replicates did your group have?________________ Why is it good to have more than one replicate?

Exercise 1.2

Letâs Graph

In this exercise, you will be graphing the data that you collected in exercise 1.1.

1. In exercise 1.1, you identified the independent and dependent variables. Which one goes on the X axis of the graph and which goes on the Y axis?

2. Will you make a line or a bar graph of your data? Explain why you chose this type of graph.

3. You will need to use excel to generate a graph of your data. On this graph, you will need to label the title, independent variable, dependent variable and possibly the legend. You will need to select an appropriate scale so the data is spread out on the graph.

*Consult with your instructor to see how he/she would like for you to submit your graph. You might work on it in class and submit it through D2L or you might submit it at a different time. If you are taking the online version of the class, you will need to use Excel or word to make the graph.

Exercise 1.3

You will need to get the data under exercise 1.3 in the protocol sheet to complete these sections.

1. What is the dependent variable?

2. What is the independent variable?

3. Which, if any, of these individuals has diabetes? ___A or B ___?

4. What data do you have to support your hypothesis?

5. Construct a graph showing the time after eating each group had the greatest blood glucose levels.

Some of you will have seen Starship Troopers, a moviebased upon a novel by Robert Heinlein. The film deviates from thebook in some ways, for example the book describes a visit to aplanet to resupply the dropships used in combat operations by theM.I. (mobile infantry). Heinlein describes this visit in the book;a portion of the novel is reproduced on the followingpage.

The followig passage contains two concepts we havediscussed in class in relation to the effects of mutation onpopulations, one positive and one negative. Describe the twomutation related concepts Heinlein discusses. You must describethese concepts as a biologist - you must use the technical terms wehave used in class properly and explain the positive and negativeeffect of mutation on the evolution and health of apopulation.

(a) What is the positive effect of mutation as describedby Heinlein?

(I.E., what does Heinlein describe as a benefit ofhaving more mutations)

(b) What is the negative effect of mutation as describedby Heinlein?

(I.E., what does Heinlein describe as a problem ofhaving more mutations)

I never have learned the co-ordinates of Sanctuary,nor the name or catalogue number of the star it orbits - becausewhat you donât know, you canât spill; the location isultra-top-secret, known only to shipâs captains, piloting officers,and such ... and I understand, with each of them under orders andhypnotic compulsion to suicide if necessary to avoid capture. So Idonât want to know. With the possibility that Luna Base might betaken and Terra herself occupied, the Federation kept as much ofits beef as possible as Sanctuary, so that a disaster back homewould not necessarily mean capitulation.

But I can tell you what sort of a planet itis. Like Earth, but retarded.

Literally retarded, like a kid who takes tenyears to learn to wave bye-bye and never does manage to masterpatty cake. It is a planet as near Earth as two planets can be,same age according to the planetologists and its star is the sameage as the Sun and the same type, so say the astrophysicists. Ithas plenty of flora and fauna, the same atmosphere as Earth, nearenough, and much the same weather; it even has a good-sized moonand Earthâs exceptional tides.

With all these advantages it barely got awayfrom the starting gate. You see, itâs short on mutations; it doesnot enjoy Earths high level of natural radiation.

Its typical and most highly developed plantlife is a very primitive giant fern; its top animal life is aproto-insect which hasnât even developed colonies. I am notspeaking of transplanted Terran flora and fauna - our stuff movesin and brushes the native stuff aside.

With its evolutionary progress held down toalmost to zero by lack of radiation and a consequent mostunhealthily low mutation rate, native life forms of Sanctuary justhavenât had a decent chance to evolve and arenât fit to compete.Their gene patterns remain fixed for a relatively long time; theyarenât adaptable - like being forced to play the same bridge handover and over again, for eons, with no hope of getting a betterone.

As long as they just competed with eachother, this didnât matter too much - morons among morons, so tospeak. But when types that had evolved on a planet enjoying highradiation and fierce competition were introduced, the native stuffwas outclassed.

Now all the above is perfectly obvious fromhigh school biology ... but the high forehead from the researchstation there who was telling me about this brought up a point Iwould have never thought of.

What about the human beings who havecolonized Sanctuary?

Not transients like me, but the colonists wholive there, many of whom were born there, and whose descendantswill live there, even unto the umpteenth generation - what aboutthose descendants? It doesnât do a person any harm not to beradiated; in fact itâs a bit safer - leukemia and some types ofcancer are almost unknown there. Besides that, the economicsituation is at present all in their favor; when they plant a fieldof (Terran) wheat;, they donât even have to clear out the weeds.Terran wheat displaces anything native.

But the descendants of those colonists wonâtevolve. Not much, anyhow. This chap told me that they could improvea little through mutation from other causes, from new blood addedby immigration, and from natural selection among the gene patternsthey already own - but that is all very minor compared with theevolutionary rate on Terra and on any usual planet. So whathappens? Do they stay frozen at their present levels while the restof the human race moves on past them, until they are livingfossils, as out of place as a pithecanthropus in a spaceship?

Or will they worry about the fate of theirdescendants and dose themselves regularly with X-rays or maybe setof lots of dirty-type nuclear explosions each year to build up afallout reservoir in their atmosphere? (Accepting, of course, theimmediate dangers of radiation to themselves in order to provide aproper genetic heritage of mutation for the benefit of theirdescendants.)

This bloke predicted that they would not doanything. He claims that the human is too individualistic, tooself-centered, to worry that much about future generations. He saysthat the genetic impoverishment of distant generations through thelack of radiation is something most people are simply incapable ofworrying about. And of course it is a far-distant threat; evolutionworks so slowly, even on Terra, that the development of a newspecies is a matter of many, many thousands of years.

I donât know. Shucks, I donât know what Imyself will do more than half the time; how can I predict what acolony of strangers will do? But Iâm sure of this: Sanctuary isgoing to be fully settled, either by us or by the bugs. Or bysomebody. It is a potential utopia, and, with desirable real estateso scarce in this end of the Galaxy, it will not be left in thepossession of primitive life forms that failed to make thegrade.

STA 119 Lecture Notes - Lecture 7: Probability Distribution, Probability Mass Function, Random Variable

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