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Random Variables Assignments-
1) Let f be a random variable. Assume that f ≥ 0. Assume that f and f2 are independent. Prove that f is almost surely a constant.
2) Prove that two random variables are independent if and only if for every pair of Borel sets B1 and B2 the following equality holds
E(χ(B1) · χ(B2)) = E(χ(B1)) · E(χ(B2))
3) Let (?, A, µ) be a probability space. Prove that the collection of all self-independent sets is a σ-algebra. Prove that this σ-algebra is independent with A.
three experiments investigating the relation between need for cognitive closure and persuasion were performed. part of
describe the types of probability.classify the statement as an example of classical probability empirical probability
If you were the lawyer for the Collins couple how would you have countered the above argument?
In Problem 15 we collected a balanced RSS of 96 subjects from the NHANES III population using a set size of k = 8 and arm circumference as the auxiliary variable to perform the judgment rankings with the goal of making inferences about the BMI for..
What is the probability that the game will cut into the next show, that is, go past 5:00?- What is the probability of this occurring?
Calculate the standard deviation of the sample mean for samples of size 1, 4, 25, 100, 250, 500, 1000, and 5000. Graph your results with the sample size on the x axis and the standard deviation on the y axis.
Assume 85% of passengers show up, 15% will not. Airline booked 11 people for 10 seats.
Suppose that the data in Table represent approximate distribution of blood type frequency in percentage of total population.
in a certain city 30 of the families have a mastercard 20 have an american express card and 25 have a visa card.
One school found that 28.6% of all students are liberal. You wonder whether this percentage is different at your school, but don't know whether it's higher or lower. What hypotheses will you test to see if your school significantly differs from th..
A restaurant has an ice cream counter where it sells two main products, ice cream and frozen yogurt. The restaurant makes one order for ice cream and yogurt each week, and the store has enough space for 115 gallons of both products.
consider the following experiment flip a coin. if you obtain heads roll a die. if you obtain tails draw a ball from a
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