17.4.1. For Discrete Random Variables

Try these first

1. 1.

   Is the statement 'Independent variables affect each other's probability' true or false?

   Hint

   Think about how independence relates to probability.

2. 2.

   Define a discrete random variable in one sentence.

   Hint

   Consider what kind of values can be counted.

3. 3.

   What is the condition for independence between discrete random variables?

   • A: P(X
   • Y) = P(X) × P(Y)
   • B: P(X) = P(Y)
   • C: P(X|Y) = P(X)

   Hint

   Recall the equation for independence.

4. 4.

   True or False: If P(X=1, Y=2)=0.4 and P(X=1)=0.5, P(Y=2)=0.3, X and Y are independent.

   • True
   • False

   Hint

   Use the independence equation for checking.

5. 5.

   Given a joint probability table for random variables X and Y, assess their independence: X/Y 1 2; 1 0.2 0.5; 2 0.3 0.1.

   Hint

   Carefully label all calculations for clarity.

6. 6.

   Develop a scenario involving two random variables where independence simplifies decision-making. Explain the impact.

   Hint

   Think about practical applications in engineering or statistics.