2013-02-14, 20:37
#1
HEJ!
Jag har en uppgift där jag ska bestämma sannolikhetsfördelningen. Jag har fått 5 funktioner som jag ska bestämma fördelningen på.
Detta är den inledande informationen jag får:
This lab presents some of the probability distributions that are used in statistical inference.
Assume a random sample of n observations from a population that follows a normal distribution with mean µ = 0 and variance =1. For such a sample, you shall study the distributions of the four sample statistics y1, y2, y3 and y4. For the statistic y5 you assume two independent samples of sizes n and m from the same population (N(0,1)).
y1 =x ̅
y2 = ∑(x_i-μ)^2 )/σ^2
Uppgift ett
Each of the statistics follows a probability distribution that is described in the textbook. List the distribution's parameters as given by the textbook (making reference to an appropriate definition or theorem in the textbook). For each of the five statistics, state a formula for the statistic's mathematical expectation, its variance, and its standard deviation. Use these formulas to calculate the mathematical expectation, variance, and standard deviation for the statistics Y1 Y2 Y3 and Y4 when n=5 and n=20 as well as for Y5 when n=5 for the numerator and m=20 for the denominator. Present your results in a table.
Tack på förhand!
Jag har en uppgift där jag ska bestämma sannolikhetsfördelningen. Jag har fått 5 funktioner som jag ska bestämma fördelningen på.
Detta är den inledande informationen jag får:
This lab presents some of the probability distributions that are used in statistical inference.
Assume a random sample of n observations from a population that follows a normal distribution with mean µ = 0 and variance =1. For such a sample, you shall study the distributions of the four sample statistics y1, y2, y3 and y4. For the statistic y5 you assume two independent samples of sizes n and m from the same population (N(0,1)).
y1 =x ̅
y2 = ∑(x_i-μ)^2 )/σ^2
Uppgift ett
Each of the statistics follows a probability distribution that is described in the textbook. List the distribution's parameters as given by the textbook (making reference to an appropriate definition or theorem in the textbook). For each of the five statistics, state a formula for the statistic's mathematical expectation, its variance, and its standard deviation. Use these formulas to calculate the mathematical expectation, variance, and standard deviation for the statistics Y1 Y2 Y3 and Y4 when n=5 and n=20 as well as for Y5 when n=5 for the numerator and m=20 for the denominator. Present your results in a table.
Tack på förhand!
