Provide solution using Matlab code if possible:

Assume that you generate a random variable X drawn from the uniform distribution on [0,1].

For example, you might define X = rand().

Now define two real (nonrandom) numbers p and q, both in [0,1].

Define event A to be the event that X <= p.

Define event B to be the event that X >= (1-q).

For which values of p and q are A and B independent?

Assume that you roll 2 different die, each with 11 sides (ranging in value from 1 to 11).

Now define event C to be the event that you roll doubles.

And define event D to be the event that the sum of the die-values is 12.

What is the probability of C?

What is the probability of D?

What is the probability that both C and D occur?

Are events C and D independent??