Explain the characteristics of different extreme weather events.

Explain how climate models aid in predicting future climate.

Explain the role of India in Climate Policy formulation and deliberations.

Explain the different indicators of Anthropogenic Climate Change

 Cramer -Rao inequality

Hamiltonian function

Central Limit theorem

Central Limit theorem

Euler-Lagrange equation

 Examine the following functions for maxima and minima:
a) 
b) 

Consider the following simple problem:
min. 
Subject to 

x₁,x₂...x_n is a random sample from a Normal population N(,1). Show that
, x_i² is an unbiased estimator of 

Discuss the features of chi square, t and f test?

Find the extremal for the functional
J(.)= ,
Boundary condition x(t₀) = 0, -x(t_f) = 2
t₀=0, t_f=2

What are isoperimetric problems?

Given the input matrix and the final demand vector:
A =  d = 

a) Explain the economic meaning of the elements 0.30,0 and 200
b) Explain the economic meaning of (if any) of the third column sum
c) Explain the economic meaning of (if any) of the third row sum
d) Write out the specific input-output matrix equation for this model
e) Find the solution output levels of the three industries using Cramer's rule.

 Explain the economic meaning of the elements 0.30,0 and 200

Given the input matrix and the final demand vector:
A =  d = 

Using Taylor's approach, find Taylor's series expansion for the function:
f(x,y,z)=x,y,z around the point (1,1,1)

Explain Taylor's theorem to polynomial expansion.