Probability-Characteristic Function (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 3 of 3

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Question number: 1

» Probability » Characteristic Function

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Obtain the characteristic function of X whose pdf is

f(x)=λπ.1λ2+(xμ)2,<x<

Explanation

The characteristic function of X is

E(eitx)=λπeitxλ2+(xμ)2dx

Let assume x-µ = v, then dx = dv

=λπ… (403 more words) …

Question number: 2

» Probability » Characteristic Function

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Find the density function of X whose characteristic function Φ (t) is given by:

ϕ(t)={1 t , t 10, t >1

Explanation

Rewrite the characteristic function Φ (t)

ϕ(t)={1t,0<t11+t,1<t<00,t>1ort<1

ϕ(t)={1… (236 more words) …

Question number: 3

» Probability » Characteristic Function

Appeared in Year: 2009

Essay Question▾

Describe in Detail

Find the density, if its characteristic function is

ϕ(t)={1 t , t 10,otherwise

Explanation

Rewrite the characteristic function Φ (t)

ϕ(t)={1t,0<t11+t,1<t<00,t>1ort<1

ϕ(t)={1… (236 more words) …

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