**(a) Monte Carlo Technique**

(i) Generate random numbers µ from (0, 1)

(ii) Generate random observations from any desired probability distribution.

**(b) Method of Inversion**

(i) Generate a random number µ from (0, 1)

(ii) Find the distribution function F(x) of the random variable X

(iii) Set F(x _{i}) = u ^{i}

X _{i} = f _{-1}(u _{i})

which gives the random observation from the probability distribution of X.

**(c) Rejection Method**

Let the pdf f(x) over a finite interval [A, B] and C be the mode of the distribution.

(i) Generate two random numbers u_{1} and u_{2} from (0, 1).

(ii) Take a point on x-axis as

p = A+ (B- A) u_{1}

(iii) Take a point on the vertical axis as

q = c.u^{2}

(iv) If q ≤ f (p) accept the pair (p, q) else reject µ pair. All the rejected pairs lie outside the boundary of the curve j(x).