2. If A C B, then m*(A) < m*(B). 3. If A = Q' n (0,1), then A is measurable. %3D
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.show that if A occurs in a larger proportion of the cases where B is than wgere B is not, then B will occur in a larger proportion of cases where A is than where A is not.Show that: if A occurs in a larger proportion of cases where B is than where it is not, then B will occur in a larger proportion of cases where A is than where A is not.
- Suppose X and Y are random variables with E[XY ] = 6, E[Y ] = 4 and E[X] = 5 Find Cov(X; Y )Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. n = 4, x = 1. n = 2, x = 2 n = 2, x = 0.Suppose that X and Y are unknowns with E ( X ) = 12 and E ( Y ) = 20. If E ( X Y ) = 225, then what is the covariance of X with Y?
- To test this null hypothesis, we compute t using a special case of the formula. state the formula?When a certain glaze is applied to a ceramic surface, the probability is 5% that there will be discoloration, 20% that there will be a crack, and 23% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise. a) Let pX denote the success probability for X. Find pX. b) Let pY denote the success probability for Y. Find pY. c) Let pZ denote the success probability for Z. Find pZ. d) Is it possible for both X and Y to equal 1? e) Does pZ = pX + pY? f) Does Z = X + Y? Explain.If θ̂ is a point estimator of θ, prove that MSE(θ̂) = V(θ̂) + (B(θ̂))2