# 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

Appeared in Year: 2014

### 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

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2010

### 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

Appeared in Year: 2009

### 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

Appeared in Year: 2013

### 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

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2011

### 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

Appeared in Year: 2011

### 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

Appeared in Year: 2015

### Describe in Detail

Let X have pdf

Obtain the cdf of Y = X ^{2}.

### Explanation

… (61 more words) …