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

Essay Question▾

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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

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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

P(Xμkσ)11k2

or P(Xμ<k)>1… (76 more words) …

Question number: 88

» Probability » Elements of Measure Theory

Appeared in Year: 2012

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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

=P(ABC)

=1P(ABC)c

=1P(… (82 more words) …

Question number: 89

» Probability » Standard Probability Distributions » Binomial

Appeared in Year: 2010

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Let X 1, X 2, …, X m be i. i. d. random variables with common p. m. f.

P(X=k)=(nk)pk(1p)nk,k=0, 1,2,,n;0<p<1

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

Essay Question▾

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Explain how to carry out the chi-squared test for H0:σ2=σ02 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

H0:σ2=σ02Vs.HA:σ2σ02

The null hypothesis is test… (557 more words) …

Question number: 91

» Probability » Standard Probability Distributions » Gamma

Appeared in Year: 2011

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Let

f(x)=1Γnβnxn1exβ,x>0,n>0,β>0

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

0f(x)dx=1

0f(x)dx=01… (380 more words) …

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