Statistical Methods-Measures of Location (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 6 of 7

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Question number: 1

» Statistical Methods » Measures of Location

Appeared in Year: 2010

Essay Question▾

Describe in Detail

A cyclist pedals from his house to his college at a speed of l0 km per hour and back from the college to his house at 15 km per hour. Find the average speed.

Explanation

Given that a cyclist pedals from his house to his college at a speed of l0 km per hour and back from the college to his house at 15 km per hour. Assume that the distance between the house to college is d. Here the average speed is finding by… (90 more words) …

Question number: 2

» Statistical Methods » Measures of Location

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Let F n (x) be the distribution function define by

Fn(x)={0;xnx+n2n;n<x<n1;xn

Is the lim F n (x) a distribution function? If not, why?

Explanation

The function F n (x) is a distribution function if

limnFn(x)=limnx+n2n

=limn(x2n+12)

=121

By the definition… (31 more words) …

Question number: 3

» Statistical Methods » Measures of Location

Appeared in Year: 2011

Essay Question▾

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Let Z be a random variable with p. d. f. f (z). Let z α be its upper α th quantile. Show that if X is

a random variable with p. d. f. 1σf(xμσ) then σz α +µ is the upper α th quantile of X.

Explanation

Let Z be a random variable with p. d. f. f (z). Given that the quantile of z is defined as

P[Z<z]=zf(t)dt=zα

X is a random variable with p. d. f.… (126 more words) …

Question number: 4

» Statistical Methods » Measures of Location

Appeared in Year: 2010

Essay Question▾

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Show that for any discrete distribution, standard deviation is not less than mean deviation from mean.

Explanation

Here, we show that standard deviation is greater than mean deviation from mean.

S. D. ≥ mean deviation from mean

(S. D. ) 2 ≥ (mean deviation from mean) 2

Let x 1, x 2, …, x n are n observations in a set have frequency f 1… (233 more words) …

Question number: 5

» Statistical Methods » Measures of Location

Appeared in Year: 2015

Essay Question▾

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Let X have the probability density function

f(x)={(α+1)xα;0<x<1,α>10;otherwise

Find the mean, geometric mean and harmonic mean.

Explanation

Then mean is

E(X)=01xf(x)dx

=(α+1)01xα+1dx

=(α+1)[xα+2α+2]01… (159 more words) …

Question number: 6

» Statistical Methods » Measures of Location

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

x=w1x1+w2x2++wnxnw1… (92 more words) …

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