Differentiate between 10 g normal distribution and binomial distribution.

Let the stress in a member X and the area of section Y be independent random variables, the force Z in the member is given by

Z=XY.

It is given that

fx 0 x 4.

1/9 0 Y 9.

Determine the PDF (Partial differential function) of Z.

Write down the mathematical expression of probability function of Binomial distribution. Explain Poisson distribution and Gamma distribution.

Discuss the principle of De-Morgan's law. Write the basic axioms of probability.

Discuss the first order second moment method (FOSM).

Explain the Level 2 reliability methods.

What is meant by local minimum, local maximum, and global or absolute minimum in a single variable optimization problem?

Using inverse transformation technique, develop expressions for generating random deviates of Y having following distributions:

Uniform distribution

Exponential distribution

What is the use of sample size in study of distribution of strength in flexure?

Discuss the Monte-Carlo method. Write its various applications.

What do you mean by slack variable and surplus variable in linear programming problem? What are they used for?

State any four applications of simplex method.

Give three reasons why the study of unconstrained minimization methods is important.

State the iterative approach used in unconstrained optimization.

List the different random search methods in unconstrained optimization problem.

Define independent and mutually exculusive events. Can two events be mutually exculsive and independent simultaneously? Support your answer with example.

Write short notes on any two of the following:

Variable Metric Method

Bayes' Theorem

Classical Optimization Technique

Grid and Random Method