Conditional probability of A given B has occurred: x2f(x) or E(X2) = Discrete uniform distribution X ∼ dU(N): f(k) = 1. N. , 1 ≤ k ≤ N, E(X) = N + 1 n. ) , max(0,n − Nq) ≤ k ≤ min(n, N p),. E(X) = np, Var(X) = npq. (. 1 − n − 1 1 σ φ( x − µ σ. ), E(X) = µ, Var(X) = σ2. Central Limit Theorem (CLT): if X1,,Xn are IID, E(Xi) 

Answer to: Let (X1,X2) be uniformly distributed over [0,1]*[0,2]. Uniform Distribution: Bayes' theorem is a formula used for computing conditional probability, which is the probability of

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N. , 1 ≤ k ≤ N, E(X) = N + 1 n. ) , max(0,n − Nq) ≤ k ≤ min(n, N p),. E(X) = np, Var(X) = npq. (. 1 − n − 1 1 σ φ( x − µ σ.

where x = 0,1. What is the relationship between this and the m.g.f. of the binomial distribution? Find the variance of x1+x2 when x1 ∼ f(p1 = 0.25) and x2 ∼ f(p2 

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18.440 Midterm 2, Fall 2012: 50 minutes, 100 points 1. (10 points) Suppose that a fair die is rolled 18000 times. Each roll turns up a uniformly random member of the

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2 θ 1 2. 0 otherwise n i 1 (b) Find the conditional 3. 0.25. 0.75. 1.

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4 Sep 2015 Conditional Probability is Probability P (A|B) is a probability function for any Mathematically, if x1, x2, x3, are all of the distinct possible values When you plug any CRV into its own CDF, you get a Uniform(0,

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