ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 82 - 86 of 165
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Question number: 82
» Probability » Probability of M Events Out of N
Appeared in Year: 2014
Describe in Detail
A positive integer X is selected at random from the first 50 natural numbers.
Calculate P (X + 96/X > 50).
Explanation
Total number of possible outcomes = number of ways in which the one random number can be chosen out of 50
Let Y be the event whose satisfied the relation, X + 96/X > 50
For which X we choose is
So, X takes values = 1,2, 48,49,50
Favorable | Others | Total | |
Avaible | 5 | 45 | 50 |
Choose number | 1 | 0 | 1 |
… (50 more words) …
Question number: 83
» Statistical Methods » Tests of Significance » F-Test
Appeared in Year: 2012
Describe in Detail
Indicate how you would test the hypothesis that the means of k independent normal populations are identical, clearly mentioning the null and the alternative hypotheses, the assumptions made, the test statistic used, and the critical region.
Explanation
Let there are k independent normal population with different sample size n 1, n 2, …, n k. The test of null hypothesis is that the means of k normal population is same and the alternative hypothesis is any two mean are not same.
Vs H 1: at least two mean are no
… (257 more words) …
Question number: 84
» Statistical Methods » Regression » Linear
Appeared in Year: 2011
Describe in Detail
From a bivariate data set of 4995 observations, the following quantities have been calculated:
Obtain the estimated linear regression of X on Y.
Explanation
Let the linear equation is
To solve this equation by least square method. In this approach, the residual sum of squares is minimized by partially differentiating with respect to and .
To differential this, we get the estimate of and
… (167 more words) …
Question number: 85
» Probability » Elements of Measure Theory
Appeared in Year: 2014
Describe in Detail
Suppose that all the four outcomes 0 1, 0 2, 0 3 and 0 4 of an experiment are equally likely. Define A = (0 1, 0 4), B = (0 2, 0 4) and C = (0 3, 0 4). What can you say about the pairwise independence and mutually independence of the events A, B and C?
Explanation
Given that there are four outcomes. Define A = (O 1, O 4), B = (O 2, O 4), C = (O 3, O 4)
Their intersection is and Union is AUBUC = (O 1, O 2, O 3, O 4)
P (A) = P (B) = P (C) = 1/2
P (AUBUC) =1
The events A, B and C are not pairwise independent because
… (117 more words) …
Question number: 86
» Statistical Methods » Tests of Significance » F-Test
Appeared in Year: 2013
Describe in Detail
Obtain 100 (1 -α) % confidence interval for the ratio of population variances by using two independent random samples from N (µ 1, σ 1 2) and N (µ 2, σ 2 2) under the assumption that the population means are (i) known and (ii) unknown.
Explanation
Let X 1, X 2, …, X n and Y 1, Y 2, …Y m are the samples taken from independent N (µ 1, σ 1 2) and N (µ 2, σ 2 2).
In this question the hypothesis for testing is
Let s 1 2 and s 2 2 be the estimates variances of σ 1 2 and σ 2 2 based on sample sizes n and m.
and
… (379 more words) …