Exam Questions - Discrete random variables

Exam Questions - Discrete random variables

Overview of Discrete Random Variables in Questions

  • Discrete Random Variables are crucial to understand while tackling problem sets, as they often form the basis of many questions.

  • Questions may involve the calculation of expected values, variances, and standard deviations of discrete random variables.

  • You will need to demonstrate the ability to use discrete probability distribution tables in problem-solving, a key tool when working with these random variables.

Interpreting Questions

  • Always read questions carefully to understand the context, it will help you distinguish the type of random variable involved.

  • Look out for hints in the question pointing towards independence or dependence of variables, as it may affect the calculation of variance.

Problem Solving – Expected Values

  • The expected value of a discrete random variable, denoted E(X), can be worked out using the formula: E(X) = Σ [x * P(X = x)], where P(X = x) is the probability of the outcome.

  • To solve questions involving expected values, establish the probability of each outcome and multiply each by corresponding value of the random variable, then compute the sum.

Problem Solving – Variances

  • The variance, Var(X), of a discrete random variable is calculated with the formula: Var(X) = E(X²) - [E(X)]².

  • When solving problems dealing with variance, remember to first calculate E(X) and E(X²) and then substitute these values into the formula.

Handling Linear Combinations

  • In questions dealing with linear combinations of random variables, remember that the expected value is calculated by E(aX + bY) = aE(X) + bE(Y).

  • To find the variance of two independent random variables, you can use Var(aX + bY) = a²Var(X) + b²Var(Y). If X and Y aren’t independent, the covariance or correlation is required.

Use of Tables

  • Use of tables is very common when dealing with discrete random variables. Become comfortable with creating and interpreting such tables.

  • Tables can clearly show all possible outcomes and their associated probabilities, vital for calculations of expected values and variances.

Endnote

  • Understanding the context and equations associated with discrete random variables is crucial for success in problem sets and assessments.

  • Regular practice of these concepts is key to strengthen your problem solving skills within this complex topic.