SCO 2550 Lecture Notes - Lecture 4: National Organization For The Reform Of Marijuana Laws

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bluemuskrat45

25 Dec 2017

School

UMN

Department

Supply Chain and Operations

Course

SCO 2550

Professor

Papp Oliver

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An infinite set of v+lues on + finite interv+l. Whether you include endpoints or not, the prob+bility between + +nd b(including + +nd b or not) is the s+me. C+nnot do this since + must be in functions dom+in. Bell sh+ped curve with equ+l me+n, medi+n, +nd mode. Don t need to know function, h+s no +nti-deriv+tive, we will use + t+ble. All v+lues st+rt +t the me+n, +dd 0. 5 for +bsolute v+lues. We do this to convert into + better form. The columns go to the first decim+l pl+ce, +nd the rows go to the second decim+l pl+ce. The resulting number tells the percent+ge from z st+nd+rd devi+tions +w+y. You c+n +lso subtr+ct prob+bilities to get the desired percentile r+nge. Finding if d*t* is in * norm*l distribution. Visu+lly look +t + histogr+m to see if it s + bell curve. Find the interqu+rtile r+nge/st+nd+rd devi+tion, should be +bout 1. 3.

Related Questions

you must use matlab or octave program. others are not allowed T.T. please use only above the two program to get solution.

Problem 3: The Inverse Transformation Method A general method for simulating a RV having a continuous distribution called the inverse transformation method is based on the following result (see also Section 10.2 of the textbook and Quiz 2) Proposition 2.1. The Inverse Transformation Method). L UN U(0,1). For any continuous et distribution function F, X F-1(U) has distribution function F. (F-1(ar) is defined to equal that value y for which F(y) r.) In order to simulate X n Exp(1), for example, generate an U U(0,1) and let X log(1 -U) (see Quiz 2(c)). In fact, X log(U) is also Exp(1), since 1 U (0,1). Since X Exp(A) if X Exp(1) (why?), it follows that log(U)A has an Exp(1) distribution. This can be easily illustrated in Octave xi -log Grand (100,1)); 100 random samples from Exp (1) x2 -log (rand (100, 1))/2; 100 random samples from Exp(2) x3 -log Grand (100, 1))*2; 100 random samples from Exp(0.5) [mean (x1) mean(x2) mean (x3)] check their mean values In addition, Y X Gamma(n, A) if X Xn are i.i.d. Exp(A). Therefore, if Un are i.i.d. U(0, 1), log (Ui) 1 log Ui Gamma(n, A) (1) i-1 i-1 (a) Write an Octave code to generate 100 random samples from Gamma(10, A) by using the inverse transformation method (1). Let A 0.5, 1, 2. Plot histograms for the Gamma random samples. Octave also has a built-in gamma RV generator gamrnd (google it for reference!). Generate 100 random samples of Gamma(10, A) using gamrnd, make histograms, and compare two results. (b) As a function of U U(0, 1), create a new RV W with CDF F(w) 1 e-ti (w 0). (This is Quiz 2 (b).) Write an Octave code to generate 100 random samples of W F using the inverse transformation method (c) Consider a method for generating Weibull(a,B) RVs that have the following CDF F(z) exp(-ar 0 z oo, a Note that W in (b) is in fact Weibull(1,2). Write an Octave function myweibrnd.m that will generate n random samples for given parameters a and B. It should have the following format function CRJ myweibrnd n, alpha, beta) this function receives sample size n and parameters alpha and beta as input arguments and return R Ca vector of n random samples) (put your code here) Using your myweibrnd function, generate 1000 simulated values when (i) (a, B) (1,2) and (ii) (a,B) (2,1), respectively. Plot histograms and estimate their mean and variance

Show transcribed image text Problem 3: The Inverse Transformation Method A general method for simulating a RV having a continuous distribution called the inverse transformation method is based on the following result (see also Section 10.2 of the textbook and Quiz 2) Proposition 2.1. The Inverse Transformation Method). L UN U(0,1). For any continuous et distribution function F, X F-1(U) has distribution function F. (F-1(ar) is defined to equal that value y for which F(y) r.) In order to simulate X n Exp(1), for example, generate an U U(0,1) and let X log(1 -U) (see Quiz 2(c)). In fact, X log(U) is also Exp(1), since 1 U (0,1). Since X Exp(A) if X Exp(1) (why?), it follows that log(U)A has an Exp(1) distribution. This can be easily illustrated in Octave xi -log Grand (100,1)); 100 random samples from Exp (1) x2 -log (rand (100, 1))/2; 100 random samples from Exp(2) x3 -log Grand (100, 1))*2; 100 random samples from Exp(0.5) [mean (x1) mean(x2) mean (x3)] check their mean values In addition, Y X Gamma(n, A) if X Xn are i.i.d. Exp(A). Therefore, if Un are i.i.d. U(0, 1), log (Ui) 1 log Ui Gamma(n, A) (1) i-1 i-1 (a) Write an Octave code to generate 100 random samples from Gamma(10, A) by using the inverse transformation method (1). Let A 0.5, 1, 2. Plot histograms for the Gamma random samples. Octave also has a built-in gamma RV generator gamrnd (google it for reference!). Generate 100 random samples of Gamma(10, A) using gamrnd, make histograms, and compare two results. (b) As a function of U U(0, 1), create a new RV W with CDF F(w) 1 e-ti (w 0). (This is Quiz 2 (b).) Write an Octave code to generate 100 random samples of W F using the inverse transformation method (c) Consider a method for generating Weibull(a,B) RVs that have the following CDF F(z) exp(-ar 0 z oo, a Note that W in (b) is in fact Weibull(1,2). Write an Octave function myweibrnd.m that will generate n random samples for given parameters a and B. It should have the following format function CRJ myweibrnd n, alpha, beta) this function receives sample size n and parameters alpha and beta as input arguments and return R Ca vector of n random samples) (put your code here) Using your myweibrnd function, generate 1000 simulated values when (i) (a, B) (1,2) and (ii) (a,B) (2,1), respectively. Plot histograms and estimate their mean and variance

burgundywhale451

For a finite continuous charged object we can use integration tofind the electric potential at a point. As is the case for anyfinite charge distribution, the value of the electric potential canbe chosen to be zero at any reference point which is sufficientlyfar from the distribution. I.e. One can (and usually does) chooseV_(infinity) = 0 at r = infinity.

Consider a rod of length L extending from the origin along thepositive x axis, and a point P located at x = -D, which is adistance D from the origin. The task is to find the electricpotential (voltage) at the point P.

ChargedRod

The above Figure shows the rod. Highlighted is one small piece ofthe rod which is located at a position x and has length (dx). Note:In answers below, if you want to include dx, it is good practice toput (dx) in parentheses.

(a) Suppose that the rod is uniformly charged to a value Q. Writethe expression for the linear charge density, using the symbolsalready defined.
lambda = 1Click here to preview your answer.

(b) The small piece of the rod has length dx. In terms of symbolsL, x, (dx), D, Q and constants, what is the infinitesimal charge onthe rod? You may need to enclose dx in parentheses for it todisplay properly.
dq = 2Click here to preview your answer.

c) What is the distance from the point to the small piece of therod? Answer in terms of symbols x, L, D, (dx) and constants.
3Click here to preview your answer.

(d) What is the infinitesimal voltage produced at point P from thisdq? Answer in terms of symbols k, Q, x, L, D, (dx) andconstants.
dV = 4Click here to preview your answer.

(e) The final step would be to integrate this result. What are thelower 5Click here to preview your answer.
and upper 6Click here to preview your answer. limits on theintegration? Answer in terms of symbols x, L, D, (dx) andconstants.

Note that if the charge of the rod had not been uniform, we wouldneed to know lambda as a function of x and use that in place of(Q/L).

1. If an individual has a genotype of Bb, what types of gametes (sperm/egg) could they produce?
A) B
B) b
C) B or b
D) Bb, BB, bb
E) Bb

2. Which of the following statements is true about phenotypic plasticity, i.e., phenotype variation that is the result of genotype by environment interactions?
A. Phenotypic plasticity is only favored when the parental environment is a good predictor of the offspring environment
B. Since the trait expression of a genotype varies across environments, it cannot respond to selection
C. A variable environment is required for phenotypic plasticity to be selected for
D. A single trait can only ever be plastic or non-plastic within a species
E. Phenotypic plasticity can only occur within a single generation, never across generations

3. With large numbers of genes contributing to variation for a phenotypic trait (e.g. height in humans), the population approaches what kind of distribution for that trait?
A. Mendelian
B. Exponential
C. Binomial
D. Normal
E. Continuous

4. A classic example of phenotypic plasticity is caste determination in social insects. Whether a female ant becomes a worker, soldier, or queen is determined by the food she is fed. Would you say this this an example of G, E, or GxE?

5. In an infinite population, the frequency of the A allele is 0.3 and the frequency of the a allele is 0.7. What is the frequency of heterozygotes?
A. .10
B. .21
C. .30
D. .42
E. .70

6. Blue eyes are a recessive trait caused by an autosomal allele. If there are 180 people with blue eyes in a population of 500 people, what is the frequency of the brown-eye allele? (Assume HWE)
A. .36
B. .40
C. .50
D. .60
E. .64

7. Imagine flower color in diploid roses is determined by a single gene with two alleles, white and red, which are co-dominant so that heterozygotes are pink. Frank is colorblind and can only discriminate between white and colored roses, and knows that his population has 18 white roses and 182 non-white roses. How many of Frankâs roses are pink? (Assume HWE.)
A. 18
B. 21
C. 42
D. 84
âE. 100

8. Imagine flower color in diploid roses is determined by a single gene with two alleles, white and red, which are co-dominant. If Eva's population has 250 white roses, 500 pink roses, and 250 red roses, what is true about this population?

A. It is not in Hardy-Weinberg equilibrium
B. It is under balancing selection
C. It is connected to another population by migration
D. It is in Hardy-Weinberg equilibrium
ââE. White is a recessive lethal

9. 9% of a population is unable to taste the compound PTC, which is a recessive trait. Assuming HWE, if two carriers of the non-tasting allele had a baby what is the probability that it would be unable to taste PTC?
A. 0.09
B. 0.25
C. 0.30
D. 0.50
E. 0.70

10. (Adapted from: Christensen, A. C. (2000). Cats as an aid to teaching genetics. Genetics, 155(3), 999-1004.) ss cats have no white fur, Ss cats generally have <50% white fur, and SS cats generally have >50% white fur (cats who are 100% white are scored as dominant white and can't be scored for piebald spotting). The S allele is incompletely dominant, but variably expressed, so there is a more-or-less continuous gradient of white pigmentation in populations. You and your friends score all non-white cats up for adoption: http://www.adoptapet.com/cat-adoption/search/50/miles/48824 and find there are 160 with >50% white fur, 350 with <50% white fur, and 490 with no white fur. Which of the following statements is definitely true:

A. The population is in Hardy-Weinberg equilibrium
B. The population is not in Hardy-Weinberg equilibrium
C. There is selection acting on the population
D. It is impossible to know if the population is in Hardy-Weinberg equilibrium
E. Fur color is not a heritable trait and therefore cannot evolve

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SCO 2550 Lecture Notes - Lecture 4: National Organization For The Reform Of Marijuana Laws

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