# Happiness and Being in a Relationship Let X, Y be two Bernoulli random variables and let...

###### Question:

Happiness and Being in a Relationship Let X, Y be two Bernoulli random variables and let p = P(X = 1) (the probability that X = 1) q = P(Y = 1) (the probability that Y = 1) r = P(X = 1, Y = 1) (the probability that both X = 1 and Y = 1). Let (X1,Y1),...,(Xn, Yn) be a sample of n i.i.d. copies of (X,Y). Define and do not assumer = pq. = 3 X.Y.. We would like to know whether the facts of being happy and being in a relationship are independent of each other. In a given population, 1000 people (aged at least 21 years old) are sampled randomly with replacement and asked two questions: "Do you consider yourself as happy?" and "Are you involved in a relationship ?". The answers are summarized in the following table: Happy Not happy 205 179 In a relationship Not in a relationship 301 315 Denote by p, and r the true proportions or people that are happy, in a relationship, and both happy and in a relationship, respectively. Compute the values of p, and f. p =

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