09/14/23

(a) Determine the distribution of Z = X + Y if X ∼ f1(x) and Y ∼ f2(y) are independent. (b) Assume that X and Y both follow a uniform distribution on [0, 1], determine the distribution of Z = X + Y.
Note: the 1 and 2 in f1(x) and f2(x) are subscripts. This is introduction to Loss Models
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09/06/23

Testing: H 1 : χ 2 ≠ 7.46 Your sample consists of 41 subjects, with a variance of 2.48. Calculate the test statistic, rounded to 2 decimal places. χ 2 =
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03/29/23

stats 1000 sampling distribution of sample proportion

Suppose that 10% of the population of college students is left-handed. A classroom hasbeen built with 15 “lefty seats” (e.g. seats that have the built-in desk on the left rather than theright).(a)... more
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05/24/21

sufficient statistics
Suppose n i.i.d. random variables are generated from the CDF F. Show that the order statistics X(1), . . . , X(n) is sufficient.
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10/26/20

Order statistics
Consider the following function:X~U[1,4] and Y~[1,4]X and Y are independent. Let U be the maximum of X and Y. Give the density function of U.a)1/9(u-1), 1<u<5b)2/9(u-1), 1<u<5c) none of... more
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03/03/20

Uniformly Minimum-Variance Unbiased Estimator
1. Let X1, . . . , Xn ∼ iid Gamma(α, θ) with α known. (a) Find the uniformly minimum-variance unbiased estimator (UMVUE) for θ. (b) Determine if the UMVUE is efficient. (c) Determine if the UMVUE... more
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04/12/18

Order Statistic
I have had hard time figuring out how to convert the uniform order statistic pdf into a beta distribution like how alpha and beta are determined.   If you answer this question, that would be... more
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11/24/14

Identify the test statistic and P Value
Researchers conducted an experiment to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group of 23 people who drank ethanol and another... more
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11/20/14

probability distributions
Assume that we have assessed probability distributions for two discrete uncertain quantities: Variable 1 and Variable 2, and that they are probabilistically dependent (mutually relevant). How many... more
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