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!ft*,= ) !. Therefore, using a basis of GDP per capita at purchasing power parity (PPP) is arguably more useful when comparing living. Then p = P(X = 1) = P(A) is the probability that the event A occurs For example, if you flip a coin once and let A = {coin lands heads}, then for X = I{A}, X = 1 if the coin lands heads, and X = 0 if it lands tails Because of this elementary and intuitive coinflipping example, a Bernoulli rv is sometimes referred to as a coin flip.

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Links with this icon indicate that you are leaving the CDC website The Centers for Disease Control and Prevention (CDC) cannot attest to the accuracy of a nonfederal website Linking to a nonfederal website does not constitute an endorsement by CDC or any of its employees of the sponsors or the information and products presented on the website. *, *,%*,#0/1*2 %' 3 =@?BACDE FGIH 3J H 7KDLNMPO OQ R8S S T U V'W6XZYY \^_XZ\ ` V XbacV W'd)eCfcghCV'a^geCi fcd)Yj8geCi kmlonqpsrutvkmlonqw. Q C x g Ȃǂ Љ Ă ܂ B 1 x A ɏo Ă ܂ I 18 N6 23 h @ l Z b V B.

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P) •Dual function is q (µ) = inf p (u) µ u = p (µ), u⌦ m ⇤ ⌅ − − where p is the conjugate of p •Assume p is proper convex and strong duality holds, so p (0) = w ⇤ = q ⇤ = sup µ m ⇤ ⌦ −p (−µ) ⌅ Let Q ⇤ be the set of dual optimal solutions, Q ⇤ = ⇤ µ ⇤ p (0) p (−µ)=0 ⌅ From. The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring The expected value of X is usually written as E(X) or m E(X) = S x P(X = x) So the expected value is the sum of (each of the possible outcomes) × (the probability of the. L o s p h b r g * % H Ô ä ;.

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Kp(x k)} b sum{p(x k)} = aE(X) b Variance We often seek to summarize the essential properties of a random variable in as simple terms as possible The mean is one such property Let X = 0 with probability 1 Let Y = 2 with prob 1/3 1 with prob 1/6 1 with prob 1/6.