University:
York University
Course:
MATH 1131 | Introduction to Statistics I
Academic year:

2022
Views:

172

Pages:

3
Author:

Niklas

Find: The joint probability distribution. The conditional probability of R given G = 5. The conditional probability of G given R = 6. The covariance between R and G. Table: G 4 5 6 7 Total 3 0.09 0.12 0.15 0.04 0.4 4 0.12 0.16 0.20 0.05 0.53 5 0.03 0.04 0.05 0.01 0.13 Total 0.24 0.32 0.40 0.10 1 Calculations: Joint probability distribution: The table itself represents the joint probability distribution of R and G. Conditional probability of R given G = 5: P(R|G=5) = P(R∩G=5) / P(G=5) = 0.16 / 0.32 = 0.5 Conditional probability of G given R = 6: P(G|R=6) = P(R∩G=6) / P(R=6) = 0.20 / 0.40 = 0.5 Covariance between R and G: Cov(R,G) = E[RG] - E[R]E[G] = 5.25 - 4.25 * 4.8 = 0 Exercise 2: A bag contains 21 pieces of candy, of which 12 are peppermints and 9 are butterscotch. Let X be the number of peppermints in a sample of 5 pieces of candy selected at random and without replacement from the bag. Suppose you want to find the probability the number of peppermints is exactly 2. Which probability distribution among the following would you use? Why? Binomial Uniform Poisson Hypergeometric