Q1.If X is random variable denoting the sum obtained in rolling a pair of fair dice, determine its probability mass function.

Q2. Find the distribution function for the random variable x where probability density is given by f(x)={x; for 0

Q3.A random variable x has the probability density f(x) ={ 0, x<0

{ e^-x, x>=0

Find the probability for

(i) 1 < x <3 (ii) x> 5 (iii) The distribution function F (x).

Q4. If X is a continuous random variable with the following probability density function

f(x) ={ a(2x-x²), 0 < x < 2

(i) Find the value of "a". (ii) Find P[X>1].

Q5. A random variable X has the following probability distribution

Values of X 0 1 2 3 4 5 6 7 8

P(x) a 3a 5a 7a 9a 11a 13a 15a 17a

(i)Determine the value of a.

(ii) Find P(x<3); p(X>=3), p (0

(iii) What is the smallest value of x for which

P( X 0.5.

(iv) Also Find E(X).