# ISS Statistics Paper I (Old Subjective Pattern): Questions 41 - 46 of 165

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## Question number: 41

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2013

### Describe in Detail

Find the missing value in the table by assuming a polynomial form for y:

X | 0 | 1 | 2 | 3 | 4 |

y | 1 | 2 | 4 | - | 16 |

### Explanation

we have given that there are four values of y is given, then find the missing value of y at x = 3 using Lagrange’s interpolation polynomial because the x values is not equal interval.

The table is

X | 0 | 1 | 2 | 4 |

y | 1 | 2 | 4 | 16 |

… (241 more words) …

## Question number: 42

» Probability » Tchebycheffs Inequality

Appeared in Year: 2013

### Describe in Detail

Let X be a random variable with E [X] = 4 and E [X ^{2}] = 20. Use Chebyshev’s inequality to determine a lower bound for the probability P [0 < 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 … (75 more words) …

## Question number: 43

» Probability » Probability Generating Functions

Appeared in Year: 2014

### Describe in Detail

Let P (s) be the probability generating function associated with a non-negative, integer valued random variable X. Show that

### Explanation

To show this we use the left hand side, express the summation term

… (352 more words) …

## Question number: 44

» Probability » Bayes' Theorem

Appeared in Year: 2014

### Describe in Detail

There are three identical bags U _{1}, U _{2} and U _{3}. U _{1} contains 3 red and 4 black balls; U _{2} contains 4 red and 5 black balls; U _{3} contains 4 red and 4 black balls. One bag is chosen at random; a ball is drawn at random from the chosen bag and it is found to be red. Find the probability that the first bag is chosen.

### Explanation

Given that there are three identical bags U _{1}, U _{2} and U _{3}. Then probabilities of selecting a bag are,

Let… (173 more words) …

## Question number: 45

» Statistical Methods » Measures of Location

Appeared in Year: 2010

### Describe in Detail

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: 46

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2014

### Describe in Detail

Consider two samples as follows:

Sample 1: 1, 4, 7, 9, 16, 17, 22, 24

Sample 2: 2, 6, 10, 12, 18, 20, 26, 28, 32

Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test. [Given value of Z for α = 0.05 = 1.645, where Z is N (0, 1) ]

### Explanation

Let the sample 1 consider the population X and sample 2 consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

… (282 more words) …