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- Infographics Lab 3 4 8 Notes Download
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Earl Chemistry > SCH3U Textbook
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- SCH3U Course Notes. SCH3U Weekly Schedule. SCH4U Class Schedule. SCH4U Assessments. Section 8.3 (pp. 376-377) Section 8.4 (pp. 378-392) Section 8.5 (pp. 393-401) Summary (p. Lab Reports Math Skills Safety Conventions and Standards Safety in the Laboratory Units, Symbols, and Prefixes.
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To see a review of how to start R, look at the beginning ofLab1
Lab1 http://www-stat.stanford.edu/ epurdom/RLab.htm
Lab1 http://www-stat.stanford.edu/ epurdom/RLab.htm
Probability Calculations
The following examples demonstrate how to calculate the value of thecumulative distribution function at (or the probability to the leftof) a given number. Piezo 1 6 4 x 2.
- Normal(0,1) Distribution :
- Binomial(,) Distribution :
- Poisson() Distribution :
Exercise : Calculate the following probabilities :
- (i)
- lies between 16.2 and 27.5
pnorm(27.5,22,sd=5)-pnorm(16.2,22,sd=5)
[1] 0.7413095 - (ii)
- is greater than 291-pnorm(29,22,sd=5)
[1] 0.08075666 - (iii)
- is less than 17pnorm(17,22,sd=5)
[1] 0.1586553 - (iv)
- is less than 15 or greater than 25pnorm(15,22,sd=5)+1-pnorm(25,22,sd=5)
[1] 0.3550098
- sum(dbinom(c(20,25,30),60,prob=0.5))
[1] 0.1512435
pbinom(19,60,prob=0.5)
[1] 0.0031088
[1] 0.5445444
- less or equal is:
> ppois(5,7)
[1]0.3007083
less than is
> ppois(4,7)
[1]0.1729916
> 1-ppois(10,7)[1] 0.0985208
The following examples show how to common the quantiles of some common distributions for a given probability (or a number between0 and 1).
- Normal(0,1) Distribution :
- Binomial(,) Distribution :
- Poisson() Distribution :
Random Variable generation
The following examples illustrate how to generate random samples fromsome of the well-known probability distributions.
- Normal(,) Distribution :The first sample is from distribution and the next one from distribution.If you would like to see how the distribution of the sample points looks like ..
- Binomial(,) Distribution :
- Poisson() Distribution :
Exercise (Advanced) : Generate 500 samples from Student's distributionwith 5 degrees of freedom and plot the historgam. (Note: distribution is going to be covered in class). The correspondingfunction is rt . hist(rt(500,5),40)
Infographics Lab 3 4 8 Notes Download
- Plotting the probability density function (pdf) of a Normal distribution :
- Plotting the probablity mass function (pmf) of a Binomial distribution :
- Discrete Probabilities For a discrete random variable, you can use the probability mass to find
** Note the distinction between the continuous (Normal)and the discrete (Binomial) distrubtions.
Exercise : Plot the probability mass functions for the Poisson distribution with mean 4.5 and 12 respectively. Do you see anysimilarity of these plots to any of the plots above? If so, can youguess why ?
Exercise : Recreate the probabilities that Professor Holmes did in class (Bin(5,.4)) [You can do it in 1 command!] How would you get the expected counts?
Q-Q plot
R has two different functions that can be used for generating aQ-Q plot. Use the function qqnorm for plotting sample quantilesagainst theoretical (population) quantiles of standard normal random variable.
Infographics Lab 3 4 8 Notes Template
Example :
Infographics Lab 3 4 8 Notes Pdf
Note: Systematic departure of points from the Q-Q line (the redstraight line in the plots) would indicate some type of departure fromnormality for the sample points.
Use of function qqplot for plotting sample quantiles for onesample against the sample quantiles of another sample
A better finder attributes 5 35 download free. Example :
Exercise : Generate 100 samples from Student's distributionwith 4 degrees of freedom and generate the qqplot for thissample.
qqnorm(rt(100,df=4))Generate another sample of same size, but now from a distribution with 30 degrees of freedom and generate the q-q plot. Do you see any difference ?
qqnorm(rt(100,df=30))
qqnorm(rt(100,df=4))Generate another sample of same size, but now from a distribution with 30 degrees of freedom and generate the q-q plot. Do you see any difference ?
qqnorm(rt(100,df=30))
It should be evident to you that the t distribution is very far fromnormal, and the 30 degrees of freedom t is indistinguishable from Normal.
Infographics Lab 3 4 8 Notes Cbse
Susan Holmes2004-10-31