ISS Statistics Paper I (Old Subjective Pattern): Questions 86 - 91 of 165
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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 12) and N (µ 2, σ 22) 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 12) and N (µ 2, σ 22).
In this question the hypothesis for testing is… (451 more words) …
Question number: 87
» Probability » Tchebycheffs Inequality
Appeared in Year: 2015
Describe in Detail
Let X be a random variable with E [X] = 3 and E [X 2] = 13. Use Chebyshev’s inequality to obtain P [-2 < X < 8].
Explanation
Let X be a random variable with mean µ and variance σ 2. Then any k > 0, the Chebyshev’s inequality is
or
Question number: 88
» Probability » Elements of Measure Theory
Appeared in Year: 2012
Describe in Detail
Of three independent events A, Band C, A only happens with probability ¼, B only happens with probability 1/8 and C only happens with probability 1/12. Find the probability that at least one of these three events happens.
Explanation
Given that P (A) =1/4, P (B) =1/8, P (C) =1/12
then probability that at least one event of these three events happens is
Question number: 89
» Probability » Standard Probability Distributions » Binomial
Appeared in Year: 2010
Describe in Detail
Let X 1, X 2, …, X m be i. i. d. random variables with common p. m. f.
obtain the p. m. f. of S m = X 1 + X 2 + …. + X m.
Explanation
Let X 1, X 2, …, X m i. i. d. random variables with common p. m. f. is P (X = k) which is a binomail random variables with common parameters n and p respectively. Then, the p. m. f. of S m = X 1 +… (263 more words) …
Question number: 90
» Statistical Methods » Tests of Significance » Chi-Square
Appeared in Year: 2011
Describe in Detail
Explain how to carry out the chi-squared test for on the basis of a random sample
X 1, X 2, …, X n from N (µ, σ 2) population.
Explanation
Given that a random sample X 1, X 2, …, X n from N (µ, σ 2) population. The hypothesis is
The null hypothesis is test… (557 more words) …
Question number: 91
» Probability » Standard Probability Distributions » Gamma
Appeared in Year: 2011
Describe in Detail
Let
Show that f (x) is a probability density function. Obtain V (X).
Explanation
if X is a continuous random variable and f (x) is a continuous function of X, then f (x) is a probability density function if