1.

Determine the expected value and the variance of X = IB if the claim probability equals 0.1. First, assume that B equals 5 with probability 1. Then, let B ~ uniform(0, 10).

2.

Throw a true die and let X denote the outcome. Then, toss a coin X times. Let Y denote the number of heads obtained. What are the expected value and the variance of Y?.

3.

In Example 2.2.4, plot the cdf of X. Also determine, with the help of the obtained differential, the premium the insured is willing to pay for being insured against an inflated loss 1.1 X. Do the same by writing X = IB. Has the zero utility premium followed inflation exactly?

4.

Calculate E[ X], Var[ X] and the moment generating function m _X( t) in Example 2.2.5 with the help of the differential. Also plot the 'density'.

5.

If X = IB, what is m _X ( t)?

6.

Consider the following cdf F:

Determine independent random variables I, X and Y such that Z = IX + (1 - I) Y has cdf F, I ~ Bernoulli, X is a discrete and Y a continuous random variable.

7.

Consider the following differential of cdf F:

Find a discrete cdf G, a continuous cdf H and...