Suppose that the proportion θ of defective items in a large shipment is unknown, and the prior distribution of θ is the beta distribution for which the parameters are α = 5 and β = 10. suppose also that 20 items are selected at random from the shipment, and that exactly one of these items is found to be defective. if the squared error loss function is used, what is the bayes estimate of θ?

Evaluate cos2θ for cosθ = square root of 3/2

The birth weights of newborn babies in the unites states follow in a normal distrubution with a mean of 3.4 kg and standard deviation of 0.6 kg. reaserches interested in studying how. children gain weights decide to take random samples of 100 newborn babies and calculate the sample mean birth weights for each sample

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).