In planning the operation of a new school, one school board member claims that four out of five newly hired teachers will stay with the school for more than a year, while another school board member claims that it would be correct to say three out of five. In the past, the two board members have been about equally reliable in their predictions, so in the absence of any other information we would assign their judgments equal weight. If one or the other has to be right, what probabilities would we assign to their claims if it were found that 11 of 12 newly hired teachers stayed with the school for more than a year?
Answer to relevant QuestionsVerify that (a) b(x; n,θ) = b(n - x; n, 1 - θ). Also show that if B(x; n,θ) For x = 0,1,2,…,n, then (b) b(x; n,θ) = B(x; n,θ)- B(x- 1; n,θ); (c) b(x; n,θ) = B(n- x; n, 1-θ)- B(n- x- 1; n,1- θ); (d) B(x; n,θ) ...Use Chebyshev’s theorem and Theorem 5.3 to verify that the probability is at least 35 36 that (a) In 900 flips of a balanced coin the proportion of heads will be between 0.40 and 0.60; (b) In 10,000 flips of a balanced ...In a “ torture test” a light switch is turned on and off until it fails. If the probability is 0.001 that the switch will fail any time it is turned on or off, what is the probability that the switch will not fail during ...Prove Theorem 5.3. Theorem 5.3 If X has a binomial distribution with the parameters n and θ and Y = X/n , then E(Y) = θ and σ2Y = θ(1– θ)/n In the inspection of a fabric produced in continuous rolls, the number of imperfections per yard is a random variable having the Poisson distribution with θ = 0.25. Find the probability that 2 yards of the fabric will have ...
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