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Let An be an increasing sequence of σ-algebras whose union generates a σ-algebra S. Let µ and ν be probability measures on S such that ν is singular with respect to µ on S, but absolutely continuous with respect to µ on each An with Radon-Nikodym derivative fn . Show that fn → 0 a.s. for µ. Hint: If fn → f a.s., show by Fatou's lemma that (A f dµ ≤ ν( A) for every A ∈ S.
provide an example of each of the following types of data nominal ordinal interval and
two students are playing chess to see if they are equal in ability. the rules are that seven games will be played not
Perform a MANOVA. data set perform a MANOVA. "Group" is your fixed factor, and LDL and HDL are your dependent variables - Exploratory Data Analysis.
If I were to invite you to play the above game where I would pay you your score in dollars (1 point = 1 dollar), what should I charge you to play?
what is the critical f value for a sample of 7 observations in the numerator and 6 in the denominator? use a two-tailed
At one university, the distance to students' home is normally distributed with a mean of 200 miles and a standard deviation of 25 miles.
Population standard deviation of 4 inches. For any one person selected at random, find out the probability that their height will be?
What is the optimal solution if the annual return for U.S. Oil changes from $3 to $8 per share (everything else stays the same)? What is the value of the total return?
How large a sample is required to estimate the mean speed with a margin of error equal to 2 miles per hour with 90% confidence?
according to the national education association the mean salary of public school teachers was 35819 in 1994. assume
The theoretical probability of undesirable side effects resulting from taking Grebex is 2 in 19. If 570 people take Grebex to lower their blood pressure, how many will encounter undesirable side effects?
a salesperson either makes a sale s or does not make a sale n with each of two potential customers. the simple events
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