ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 135 - 139 of 165

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Fit the exponential curve y = a + bx to the following data

x: 0 2 4

y: 5.01 10 31.62

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Let X have the continuous c. d. f. F (x). Define U = F (x). Show that both - log U arid -log (1 - U) are exponential random variables:

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Let X ₁, X ₂, …, X ₁₂ be a random sample from a normal N (µ ₁, σ ₁²) and Y ₁, Y ₂, …Y ₁₀ be another random sample from normal N (µ ₂, σ ₂²), independently to each other. Carry out an appropriate test for testing

at 5 % level of significance. It is given that .

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You arc given the following information:

(i) In random testing, you test positive for a disease.

(ii) In 5 % of cases, the test shows positive even when the subject does not have the disease.

(iii) In the population at large, one person in 1000 has the disease. What is the conditional probability that you have the disease given that you have been tested positive, assuming that if someone has the disease, he will test positive with probability 1?

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Compute the factorial moments µ _(r) and the cumulants k _r, r = 1, 2, …. . , of Poisson distribution with parameter m.