# CS1 Actuarial Statistics

DIFFERENTIATE BETWEEN CONTINUOUS RANDOM VARIABLE & DISCRETE RANDOM VARIABLE?

Discrete random variables are random variables that take a finite number of values. For example, the outcome of rolling a die. Continuous random variables, on the other hand, can take on any value in a given interval.

WHAT IS LAW OF LARGE NUMBERS?

Law of large number states that as there is greater exposure to losses, the expected value of loss equals the actual value of loss. It basically helps in predicting the losses in a better manner.

WHAT DO YOU MEAN BY POISSON PROCESS?

This distribution models the number of events that occur in a specified interval of time, when the events occur one after another in time in a well-defined manner.

HOW MONTE CARLO SIMULATION TAKES PLACE?

A Monte Carlo simulation is used to predict the probability of a variety of outcomes when there are random variables present. Monte Carlo simulations help to explain the impact of risk and uncertainty in prediction and forecasting models.

WHAT IS THE SIGNIFICANCE OF P-VALUE?

The p-value, also called probability value, is the lowest level at which H0 (null hypothesis) can be rejected.

GIVE AN EXAMPLE OF APPLICATION OF BINOMIAL DISTRIBUTION.

Rolling a die, Tossing a coin, Number of Spam Emails per Day and Number of Fraudulent Transactions.

WHAT IS CENTRAL LIMIT THEOREM?

Central Limit Theorem gives us an approximate distribution of the sample mean when the population distribution is unknown and more importantly does not need to be known. It provides useful normal approximations to the distributions of particular functions.

WHAT DOES LEVEL OF SIGNIFICANCE DEPICT?

It is the probability of rejecting H0 when it is in fact true.

WHAT IS POSTERIOR DISTRIBUTION? HOW IS IT RELATED TO PRIOR DISTRIBUTION?

The conditional distribution given the observed data is called the posterior distribution of theta. If the prior distribution is continuous, then the posterior distribution is also continuous. Similarly, if the prior distribution is discrete, then the posterior distribution is also discrete.

WHAT IS CREDIBILITY FACTOR?

The credibility premium formula for this risk is Z*X_BAR+(1-Z)*MU where Z is a number between zero and one and is known as the credibility factor.

WHAT IS MEANT BY CAUSATION EFFECT?

Spurious correlations refers to correlation does not equal causation which means  that a change in one variable causes a change in the other — is a common misinterpretation of correlation coefficients.

WHAT IS SENSITIVITY AND SPECIFICITY?

Sensitivity refers to the true positive rate whereas specificity refers to the true negative rate. For example,the ability of a test to correctly identify patients with a disease is  sensitivity whereas specificity is the ability of a test to correctly identify people without the disease

WHAT IS R SQUARED AND ADJUSTED R SQUARE? HOW ARE THEY RELATED?

the proportion of the total variation of the responses ‘explained’ by a model, called the coefficient of determination, denoted R-square whereas adjusted r-square gives a measure of how much variability is explained by the regression model. It takes account of the undesirability of increased complexity by the r-square method.

NAME SOME DISTRIBUTIONS BELONGING TO EXPONENTIAL FAMILY.

Normal, poisson, binomial, gamma, lognormal.

DIFFERENCE BETWEEN SAMPLE VARIANCE AND POPULATION VARIANCE.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data. Sample variance is an unbiased estimator of the population variance.

WHAT IS PRINCIPAL COMPONENT ANALYSIS? WHAT IS ITS OBJECTIVE?

Principal components analysis (PCA) is used  to identify the most important variables for multivariate data sets. It is also called factor analysis, and provides a method for reducing the dimensionality of the data set.

WHAT IS A SATURATED MODEL?

A saturated model is defined to be a model in which there are as many parameters as observations, so that the fitted values are equal to the observed values.

WHAT DOES CONTINGENCY TABLE SIGNIFY?

A contingency table consists of rows and columns containing counts of sample items (people, claims etc) that are classified according to two category variables.

WHAT IS CONDITIONAL EXPECTATION?

The conditional expectation of Y given X =x is the mean of the conditional distribution of Y given X= x.

DIFFERENCE BETWEEN COVARIANCE AND CORRELATION.

Covariance refers to the relationship between two random variables in which a change in the other reflects a change in one variable which can range from -∞ to +∞. Correlation determines the degree to which two or more random variables move in sequence. Its value ranges from -1 to 1.