ISS 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

Essay Question▾

Describe in Detail

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

Explanation

The given differential equation is

dydx=x+y=f(x,y)

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

Using Euler’s method,

yn+1=yn+hf(x… (226 more words) …

Question number: 93

» Probability » Definitions and Axiomatic Approach

Appeared in Year: 2010

Essay Question▾

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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

F(x1)=P(Xx1)P(Xx2)=F(x2)

Since F… (264 more words) …

Question number: 94

» Statistical Methods » Correlation Coefficient » Partial Correlation

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

8X10Y+66=0

40X18Y214=0

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

8X10Y=66(1… (155 more words) …

Question number: 95

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2013

Essay Question▾

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

f(x,y)=xy36;x=1, 2,3;y=1, 2,3

= 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

f(x)=P(X=x)=y=13f(x… (121 more words) …

Question number: 96

» Numerical Analysis » Interpolation Formulae » Gauss

Appeared in Year: 2011

Essay Question▾

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Use mathematical induction to prove

fx+nh=i=0(ni)ifx

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

fx+nh=Enfx

=(1+)n… (44 more words) …

Question number: 97

» Probability » Expectation

Appeared in Year: 2011

Essay Question▾

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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

ya=0

aE(Xa)2=0

aE(X22aX+a2… (60 more words) …

Question number: 98

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X have pdf

f(x)={13;1<x<20;otherwise

Obtain the cdf of Y = X 2.

Explanation

FY(y)=P(Yy)=P(X2y)

=P(yXy)

=yyf(x)dx

=13yydx… (4 more words) …

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