Consider the prevalence of blood types by ethnicity in the US.

Euro. Afr. L. Am Asia Ethnicity US Pop 0.37 0.47 0.53 0.39 Caucasian 0.63 O- D.08 0.04 0.04 D.01 Lat. American 0.176 A+ 0.33 0.24 0.29 0.27 Afr. American 0.133 A- 0.07 0.02 0.02 0.005 Asian American 0.056 B+ 0.09 0.18 0.18 0.25 Figure 8.9: Prevalence of each ethnic B- 0.02 0.01 0.01 D.004 group in the US AB+ 0.03 0.04 0.04 0.07 AB- 0.01 0.003 0.003 D.001 Figure 8.8: Prevalence of each blood type for given ethnic group in the US Let X represent blood type and let Y represent ethnicity of a random person in the US. Find the joint PMF of X and Y. [Hint. Columns of the first table are conditional PMFs.]