14.4.1. Conditional PMF

Try these first

1. 1.

   What is the formula for Conditional PMF?

   Hint

   Think about how the joint and marginal probabilities relate.

2. 2.

   If P(A = 1, B = 1) = 0.4 and P(B = 1) = 0.5, what is P(A = 1 | B = 1)?

   Hint

   Use the Conditional PMF formula.

3. 3.

   What does Conditional PMF help us understand?

   • The likelihood of an event regardless of others
   • The relationship between two random variables
   • The total probability of all outcomes

   Hint

   Focus on the dependency aspect.

4. 4.

   True or False: P(X = x | Y = y) is determined solely from P(Y = y).

   • True
   • False

   Hint

   Consider what you need to calculate a conditional probability.

5. 5.

   Two variables have a joint distribution where P(X = 3, Y = 5) = 0.25, and P(Y = 5) = 0.5. Calculate P(X = 3 | Y = 5) and interpret this in a practical scenario.

   Hint

   Use the Conditional PMF formula!

6. 6.

   In medical testing, if P(Positive Test | Disease) = 0.9 and the general population probability P(Disease) = 0.01, discuss the implications if P(Positive Test) is found to be significantly different.

   Hint

   Think about sensitivity and specificity in testing.