Homework Answers
- Random variable has been defined as a function which assumes real values on the outcomes of a random experiment.In repeated performances of the random experiment,the random variable will in general assume different values with a definite probability associated with each value or interval of values.
- Variables are obtaining certain values when the values of variables are determined by the probability they are called random variables. In the sampling distribution mean has a normal shape if the population from which the samples are drawn are normal.
3. The most common measures of central tendency are the arithmetic mean,the median and the mode.
4.If the distribution is symmetric then the mean is equal to the median and the distribution will have zero skewness.
6)Variance is the measure of the spread between numbers in a data set.Formula for variance is
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Questions 1. (10 Points) What is a random variable? 2. (5 Points) Why do random variables...
Question Help Consider a random variable Y. What is the difference between the sample average Yand...
Question Help Consider a random variable Y. What is the difference between the sample average Yand the population mean? O A. Both the population mean and the sample average Ý are estimators of the central tendency of the distribution of Y O B. Both the population mean and the sample average Y are true measures of the central tendency of the distribution of Y O C. The population mean is a true measure of the central tendency of the distribution...
Please help ! Concepts to be familiar with: 1. Difference between populations (parameters) and samples (statistics):...
Please help !
Concepts to be familiar with: 1. Difference between populations (parameters) and samples (statistics): definitions and notation differences 2. Descriptive v. inferential statistics. What are they? What are their limitations? 3. Independent Variables (IVs) and Dependent Variables (DVs): definitions and how to recognize which is which in a study description 4. Discrete vs. continuous variables, apparent vs. real limits 5. Scales of measurement (N,O,I,R). Know what they are and examples of each. 6. Frequency tables: a. X, f,...
L.1) BinomialDist[1, p] random variables In what context do random variables with BinomialDist[1, p] arise? L.2)...
L.1) BinomialDist[1, p] random variables In what context do random variables with BinomialDist[1, p] arise? L.2) Expected value and Variance for the Binomial[1, p] and Binomial[n, p] random variables a) Go with a random variable X with BinomialDist[1, p Calculate Expect[X] and Var[X]. b) Go with a random variable X with BinomialDist[n, p]. Use the fact that X is the sum of n independent random variables each with BinomialDist[1, pl to explain why: Expect[x]-n p and Var[X]-np(p) L.3) Relations among...
QUESTION 4 An increase from 10% to 15% is a A 5% increase, and a 50...
QUESTION 4 An increase from 10% to 15% is a A 5% increase, and a 50 percentage point increase A 5 percentage point decrease, and a 50% decrease O A 5 percent increase, and a 5 percentage point increase 5 percentage point increase, and a 50% increase QUESTION 5 A measure of central tendency is an estimate of the middle, or center, of a distribution. True False QUESTION 6 The expected value is O The unweighted average of all possible...
Problem 7: 10 points Consider independent random variables, [Y: 1, 2, ..., ), having the same...
Problem 7: 10 points Consider independent random variables, [Y: 1, 2, ..., ), having the same Gamma distribution, with the density, .узе-2y for y > 0 Suppose that a random variable, N, does not depend on all Y, and is geometrically distributed, so that PIN = n] = n, for n=1, 2, Consider a random sum, S Y 1. Determine the marginal expectation of S. 2. Determine the marginal variance of S.
5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10...
5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10 x < 0; Fx(x) = { 0.5 0<x< 1; (1 x > 1. Is X a discrete random variable or continuous random variable? (b) Consider a CDF of a random variable Y, 1 < 0; Fy(y) = { ax + b 0 < x < 1; 11 x >1, for some constant a and b. If Y is a continuous random variable, then what...
Problem 2: 20 points 10 5 + 5) A continuous random variable (Y) has a density,...
Problem 2: 20 points 10 5 + 5) A continuous random variable (Y) has a density, fY (3e-3V for y>0 and f () 0, elsewhere. Given Y y, a discrete random variable, N, is Poisson distributed with the rate equal to y TA 1. Derive the marginal distribution of N 2. Determine the marginal expectation of N, EIN 3. Determine the marginal variance of N, Var[N]
answer all the questions, I will give u a thumb! 1.3 A portfolio consists of 10...
answer all the questions, I will give u a thumb!
1.3 A portfolio consists of 10 shares of stock A and 8 shares of stock B. The price of A has a mean of 10 and variance of 16, while the price of B has a mean of 12 and a variance of 9 The correlation between prices is 0.3. What are the mean and variance of the portfolio value? 2.1 2.1.a State the definition of the sampling distribution of...
Let Xi,. Xgs be i.i.d. random variables with equal distributaion on the 5 points -2,-1,0,1, 2)...
Let Xi,. Xgs be i.i.d. random variables with equal distributaion on the 5 points -2,-1,0,1, 2) We already know: E[Xi-0 and Var(Xi)-2 98 V 98 V Show the probability of -21 < XlX 21 OR X > 28) (3 decimal places) (1) With usage of the central limit theorem without continuity correction (2) With usage of the central limit theorem with continuity correction.
1. Draw the PDF for random variable X ~ N (ux, o3), marking clearly the location...
1. Draw the PDF for random variable X ~ N (ux, o3), marking clearly the location of jix and the approximate locations of ux tox. 2. Draw the CDF for random variable X N (ux,0), marking clearly the location of uix and the approximate locations of hx tox. 3. What are the mean and variance of a standard normally distributed variable? 4. Give a brief summary of the central limit theorem (CLT). Address, specifically (a) What limit does the CLT...
Question Help Consider a random variable Y. What is the difference between the sample average Yand the population mean? O A. Both the population mean and the sample average Ý are estimators of the central tendency of the distribution of Y O B. Both the population mean and the sample average Y are true measures of the central tendency of the distribution of Y O C. The population mean is a true measure of the central tendency of the distribution...
Please help !
Concepts to be familiar with: 1. Difference between populations (parameters) and samples (statistics): definitions and notation differences 2. Descriptive v. inferential statistics. What are they? What are their limitations? 3. Independent Variables (IVs) and Dependent Variables (DVs): definitions and how to recognize which is which in a study description 4. Discrete vs. continuous variables, apparent vs. real limits 5. Scales of measurement (N,O,I,R). Know what they are and examples of each. 6. Frequency tables: a. X, f,...
L.1) BinomialDist[1, p] random variables In what context do random variables with BinomialDist[1, p] arise? L.2) Expected value and Variance for the Binomial[1, p] and Binomial[n, p] random variables a) Go with a random variable X with BinomialDist[1, p Calculate Expect[X] and Var[X]. b) Go with a random variable X with BinomialDist[n, p]. Use the fact that X is the sum of n independent random variables each with BinomialDist[1, pl to explain why: Expect[x]-n p and Var[X]-np(p) L.3) Relations among...
QUESTION 4 An increase from 10% to 15% is a A 5% increase, and a 50 percentage point increase A 5 percentage point decrease, and a 50% decrease O A 5 percent increase, and a 5 percentage point increase 5 percentage point increase, and a 50% increase QUESTION 5 A measure of central tendency is an estimate of the middle, or center, of a distribution. True False QUESTION 6 The expected value is O The unweighted average of all possible...
Problem 7: 10 points Consider independent random variables, [Y: 1, 2, ..., ), having the same Gamma distribution, with the density, .узе-2y for y > 0 Suppose that a random variable, N, does not depend on all Y, and is geometrically distributed, so that PIN = n] = n, for n=1, 2, Consider a random sum, S Y 1. Determine the marginal expectation of S. 2. Determine the marginal variance of S.
5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10 x < 0; Fx(x) = { 0.5 0<x< 1; (1 x > 1. Is X a discrete random variable or continuous random variable? (b) Consider a CDF of a random variable Y, 1 < 0; Fy(y) = { ax + b 0 < x < 1; 11 x >1, for some constant a and b. If Y is a continuous random variable, then what...
Problem 2: 20 points 10 5 + 5) A continuous random variable (Y) has a density, fY (3e-3V for y>0 and f () 0, elsewhere. Given Y y, a discrete random variable, N, is Poisson distributed with the rate equal to y TA 1. Derive the marginal distribution of N 2. Determine the marginal expectation of N, EIN 3. Determine the marginal variance of N, Var[N]
answer all the questions, I will give u a thumb!
1.3 A portfolio consists of 10 shares of stock A and 8 shares of stock B. The price of A has a mean of 10 and variance of 16, while the price of B has a mean of 12 and a variance of 9 The correlation between prices is 0.3. What are the mean and variance of the portfolio value? 2.1 2.1.a State the definition of the sampling distribution of...
Let Xi,. Xgs be i.i.d. random variables with equal distributaion on the 5 points -2,-1,0,1, 2) We already know: E[Xi-0 and Var(Xi)-2 98 V 98 V Show the probability of -21 < XlX 21 OR X > 28) (3 decimal places) (1) With usage of the central limit theorem without continuity correction (2) With usage of the central limit theorem with continuity correction.
1. Draw the PDF for random variable X ~ N (ux, o3), marking clearly the location of jix and the approximate locations of ux tox. 2. Draw the CDF for random variable X N (ux,0), marking clearly the location of uix and the approximate locations of hx tox. 3. What are the mean and variance of a standard normally distributed variable? 4. Give a brief summary of the central limit theorem (CLT). Address, specifically (a) What limit does the CLT...
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