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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

A) 0
B) 1
C) 3
D) 2

2. If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?

A) 95%
B) 66.60%
C) 90%
D) 99%

3. Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

A) 1.638
B) 1.623
C) 2.362
D) 0.377

4. A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A) 0.2646
B) None of these
C) 0.3483
D) 0.7367

5. In statistical hypothesis tests, 'Type I error' refers to the situation in which...

A) The null hypothesis is accepted when in fact it should have been rejected
B) Both null hypothesis and alternative hypothesis are rejected
C) Both null hypothesis and alternative hypothesis are accepted
D) The null hypothesis is rejected when in fact it should have been accepted

Solutions: