Questions

1. Draw 10000 values randomly from a standard normal population and determine the following probabilities empirically (that is through a simulation).

a) P(Z < 1.8), Z ~ N(0,1).

b) P(–1.024 < Z < 1.235)

Note: The rannor(seed) function generates a value randomly from the N(0,1) population.

The seed value can be any integer. If 0 is chosen the values generated will differ for each

simulation.

2. A man pays R10 to win a R30 Kewpie doll. His probability of winning on each throw is 0.3. He must win a doll for each of his five children. Let X be the random variable indicating the number of throws required to win five dolls. Determine through simulation empirical values for the following.

a) The probability that 10 throws are needed to win the five dolls, that is P(X = 10).

b) The probability that at least ten throws will be required, that is P(X ≥ 10).

c) The expected number of throws needed to win five dolls, that is E(X).

Note: The ranuni(seed) function generates a value randomly from the UNIF(0,1) population.

In this problem, a value in the interval [0,0.3] can be considered as winning on a throw.

*see attached for Notes&examples*