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Let X be a nonempty subset of a group G.
If G = <X> and H is a subgroup of G, show that H is the normal subgroup of G if and only if x^-1Hx contained in H for all x belonging to X.
ALSO show that <X> is normal in G if and only if gXg^-1 contained in <X> for all g belonging to G.
Suppose a bullet is fired on a distant planet so that its height (in feet) after t seconds is given by h=-4t2 + 16t +5. The 2 in 4t2 is a small 2, but I don't know how to do that with my keyboard.
Multiple choice questions based on regression
Explanation to "Statistics - Probability" question Suppose you randomly place 'r' indistinguishable balls into 'n' boxes. (a) how many different ways do you have
Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function.
Normal subgroups, Second Theorem of Isomorphism, Conjugates and Cyclic Groups
Simulation of an expectation. Design a simulation exercise in R to approximate the value of E ( X^X) when X has a U [0,1] distribution. Plot the value of the approximation as the sample size goes from 1 to 10,000
G(x) = 3x^5 - 5x^4 What is the relative extreme point of g. Please explain why.
A fire detection sensor is tested for its failure rate and found to have a mean failure rate of 3.6E-2 per hour of exposure with a standard deviation of
A thin plate occupies the region x^2/4 + y^2/9 is less than or equal to 1. If the temerature of the plate is T(x,y)= x^2 + y^2 - 5y + 5, find the coldest and hottest points on the plate.
Calculate the value the test statistic
The table list data - Average Salaries of Athletes in 1991 and 2001. Use the data points to find a linear function that fits the data and then use the function to predict the average salary in 2005 and 2010.
What is the total defect rate? I came up with 6%. A randomly selected product was defective. What is the probability that it came from Plant A?
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