ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 132 - 137 of 165

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Question number: 132

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

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Appeared in Year: 2010

Essay Question▾

Describe in Detail

Show that for discrete distribution β 2 > 1

Explanation

We have to prove that

By definition of Kurtosis

Let x 1, x 2, …, x n are n observations in a set have frequency f 1, f 2, …, f n and the mean of observation is , then

Assume

… (55 more words) …

Question number: 133

» Statistical Methods » Tests of Significance » Z-Test

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Appeared in Year: 2010

Essay Question▾

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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).

Explanation

Here, you would know the standard deviation of a population but not know the mean of that population. So, you want to estimate the mean μ to within a given margin of error in a given confidence interval. The required sample size is

Margin of error E = 0.5,

1-α=0.95 →α=0.05

σ=1 and z α/2 =1.96

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Question number: 134

» Statistical Methods » Measures of Location

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Appeared in Year: 2013

Essay Question▾

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

Explanation

If x 1, x 2, …, x n are the values having weights w 1, w 2, …, w n respectively, the weight mean is

Here X is first ‘n’ natural numbers that is 1,2, 3, …, n

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Question number: 135

» Numerical Analysis » Interpolation Formulae » Lagrange

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Appeared in Year: 2015

Essay Question▾

Describe in Detail

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

x: 0 2 4

y: 5.01 10 31.62

Explanation

his is not exponential equation, it is a straight line y = a + bx

S. no

x

y

Xy

x 2

1

0

5.01

0

0

2

2

10

20

4

3

4

31.62

126.48

16

Sum

6

46.63

146.48

20

The normal equations is

Using the table, putting these values in normal equations. We get

Solving these two equations, we get the value of

… (24 more words) …

Question number: 136

» Probability » Standard Probability Distributions » Uniform

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Appeared in Year: 2011

Essay Question▾

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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:

Explanation

Let U = F (x), then the distribution function of G of U is given by

Since F is non-increasing and its continuous.

G (u) =F (F -1 (u) ) implies G (u) =u

Then the p. d. f is

Since F is a distribution function takes value in range [0,1]. Hence

… (224 more words) …

Question number: 137

» Statistical Methods » Tests of Significance » T-Test

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Appeared in Year: 2015

Essay Question▾

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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 .

Explanation

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. The test of hypothesis is

The sample size of X is n = 12 and Y is m = 10

The test is depen

… (168 more words) …

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