# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 92 - 98 of 165

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## Question number: 92

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

Using Euler’s method, compute the values of y correct upto 4 places of decimal for the differential equation with initial condition x 0 = 0, y 0 = 1, taking h = 0.05.

### Explanation

The given differential equation is

with initial condition x 0 = 0, y 0 = 1, taking h = 0.05.

Using Euler’s method,

where

So, putting the initial condition, when n = 0

… (81 more words) …

## Question number: 93

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Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Let X be a random variable defined on (Ω, A, P). Define a point function F (x) =P {ω: X (ω) ≤x}, for all xϵR. Shoe that the function F is indeed a distribution function.

### Explanation

Let x 1 < x 2. Then (-∞, x 1] ( (-∞, x 2] and we have

Since F is non decreasing, it is sufficient show that for any sequence of numbers x n ↓x, x 1 > x 2 > … > x n > …x, F (x n) →F (x). Let A k = {ω, X (ω) ϵ (x, x k] }. Then A k ϵS and also

… (123 more words) …

## Question number: 94

» Statistical Methods » Correlation Coefficient » Partial Correlation

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Appeared in Year: 2009

Essay Question▾

### Describe in Detail

The two regression lines between X and Y are 8X - 10Y + 66 = 0,40X - 18Y = 214. The variance of X is 9. Find X, Y, σ Y and ρ.

### Explanation

Given that

We know that the mean value of the given series satisfies the regression line that is

The means of X and Y is calcula

… (106 more words) …

## Question number: 95

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Let (X, Y) have a joint probability mass function

= 0, elsewhere

Find the marginal mass functions of X and Y.

### Explanation

Let (X, Y) have a joint probability mass function, the individual distribution of either X or Y is called the marginal distribution. So, the marginal mass functions of X is

and other values of f (x, y) is 0

… (68 more words) …

## Question number: 96

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Use mathematical induction to prove

### Explanation

Let ∆ i define the i th finite difference which is defined as

∆ =E-1 where E is a shift operator that is

E n f x = f x + nh

Then

… (63 more words) …

## Question number: 97

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Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Show that E (X - a) 2 is minimized for a = E (X), assuming that the· first 2 moments of X exist.

### Explanation

Assume Y = E (X - a) 2

Here we want to minimized Y for a that is

… (91 more words) …

## Question number: 98

» Probability » Distribution Function » Standard Probability Distributions

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Let X have pdf

Obtain the cdf of Y = X 2.

### Explanation

… (61 more words) …