Use the normal approximation to the binomial distribution to determine (to four decimals) the probability of getting 7 heads and 7 tails in 14 flips of a balanced coin. Also refer to Table I on pages 487– 491 to find the error of this approximation.
Answer to relevant QuestionsWith reference to Exercise 6.75, show that the Poisson distribution would have yielded a better approximation. In Exercise Suppose that we want to use the normal approximation to the binomial distribution to determine ...Using the form of the gamma function of Exercise 6.8, we can write And hence Change to polar coordinates to evaluate this double integral, and thus show that (12 ) = v p. In exercise Use the transformation technique to rework Exercise 7.2. In exercise If the probability density of X is given by And Y = X2 If the joint probability distribution of X1 and X2 is given by f(x1, x2) = x1x2 / 36 For x1 = 1, 2, 3 and x2 = 1, 2, 3, find (a) The probability distribution of X1X2; (b) The probability distribution of X1/ X2. Rework Exercise 7.30 by using Theorem 7.2 to determine the joint probability density of Z = XY2 and U = Y and then finding the marginal density of Z.
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