A fair coin is flipped twice. Let X be the number of Heads in the two tosses, and Y be the indicator r.v for the tosses landing the same way. (a) Find the joint PMF of X and Y . (b) Find the marginal PMFs of X and Y . (c) Are X and Y independent? (d) Find the conditional PMFs of Y given X = x and of X given Y = y.

UNIT 10 – Testing Hypothesis About Proportions Standardized Value (z-score, z*) – # of standard deviations an observation lies away from the mean Z = pp̂ – p = ( value – mean ) √ pq ÷ n standard deviation Hypothesis – statement about the population distribution parameter (ex: p), usually claims the parameter takes on a specific value Class Example: Study to see in bank executives are more likely to promote males than females, SRS of 48 execs were given fake resumes of 24 men & 24 women. 35 execs said they would hire the candidate; 21 male & 14 female. Is this difference evidence of discrimination Start with idea that no discrimination has occurred. If so, since males & females were equally represented in the