chapter 2 measuring risks
A Random Variable X can take only two values, 1 and 2. The probability of each random variables are: P(1) = 0.8 and P(2) = 0.2. Calculate the Expected value of X.
1.2
A coin is tossed three times. Find the probability of getting at least two heads.
1/2
Two cards are drawn from the top of a well-shuffled deck. What is the probability that they are both black aces?
1/2652
A card is chosen at random from a pack of 52 playing cards. What is the probability of a King or a Queen?
2/13
A bag contains 3 red marbles and 4 blue marbles. Two marbles are drawn at random without replacement. If the first marble drawn is red, what is the probability the second marble is blue?
2/3
Metrics
Asystem of related measures that helps us measure characteristics or qualities
In a normal distribution, the probability of any range of profitability values is calculated by finding the standard deviation under the curve in between the desired range of profitability values. T/F
FALSE
In uncertain economic situations involving possible financial gains or losses, the mean value represents the expected return from an endeavor and expresses the risk involved in the uncertain scenario. T/F
FALSE
Severity is the number of times the event is expected to occur in a specified period of time. T/F
FALSE
Calculated by multiplying each probability (or relative frequency) by its respective gain or loss.
Fair value
Which of the following is defined as the numerical average of the experience of all possible outcomes if you played the game over and over?
Fair value
Explain what is the Measure of Frequency of claims
How many claims occur per year on average
Which of the following statements is true about the risk metrics?
It allows us to measure risk, giving us an ability to control risk and simultaneously exploit opportunities as they arise.
____________ is the notion of how often a certain event will occur.
Likelihood
Probability
Process of quantifying uncertainty
Interconnected Risks
Risks dependent on each other; correlated risks.
Conditional Risks
Risks with underlying factors that may increase or decrease the risk.
Expected value is calculated by multiplying each probability or relative frequency by its respective gain or loss. T/F
TRUE
Severity
The average dollar value of a loss per claim.
distribution
The display of the events on a map that tells us the likelihood that the event or events will occur
The total number of fire claims for the two locations A and B is the same. What does this mean?
The frequency of fire claims in locations A and B is the same.
frequency
The number of losses during a specified period.
Fair value
The numerical average of the experience of all possible outcomes if you played a game over and over. Also called expected value.
The normal distribution or bell-shaped curve from statistics provides an example of a continuous probability distribution curve. While calculating the probability of the occurrence of an event, we find that the area under the curve in between the desired range of profitability values is 0.562. What does this mean?
The probability of the occurrence of the event is 56.2 percent.
Two events are considered __________ ____________if the occurrence of one event affects the occurrence of the other.
dependent events
Two events are considered _____________ ___________if the occurrence of one event does not affect the occurrence of the other event
independent events
Two events are _________ __________if the occurrence of one event precludes the occurrence of the second event.
mutually exclusive
Probability analysis
the risk manager can assign probabilities to individual and joint events
