ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 132 - 138 of 165

Describe in Detail

Show that for discrete distribution β ₂ > 1

Describe in Detail

How large a sample must be taken in order that the probability will be at least 0·95 that X _n will be within 0·5 of µ (µ is unknown and σ = l).

Describe in Detail

Find the weighted arithmetic mean of the first ‘n’ natural numbers, the weights being the corresponding numbers.

Describe in Detail

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

x: 0 2 4

y: 5.01 10 31.62

Describe in Detail

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:

Describe in Detail

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

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

Describe in Detail

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?