With reference to Exercise 3.102 on page 108, find the probability density of the random variable Z = X+ Y / 2 , which is the average of the two proportions of correct answers that a student will get on the two aptitude tests.
Answer to relevant QuestionsWith reference to exercise 3.101 on page 108, use Theorem 7.2 to find the joint probability destiny of the two random variables V = SP and W = P, and then find the marginal destiny of V. Let X1 and X2 be independent random variables having the uniform density with α = 0 and β = 1. Referring to Figure 7.2, find expressions for the distribution function of Y = X1 + X2 for (a) y ≤ 0; (b) 0< y< 1; (c) 1 < ...If, d, the diameter of a circle is selected at random from the density function (a) Find the value of k so that f(d) is a probability density; (b) Find the density function of the areas of the circles so selected. Explain why, when we sample with replacement from a finite population, the results of Theorem 8.1 apply rather than those of Theorem 8.6. Prove Theorem 8.10. Theorem 8.10 If X1 and X2 are independent random variables, X1 has a chi-square distribution with v1 degrees of freedom, and X1 + X2 has a chi-square distribution with v > v1 degrees of freedom, then X2 ...
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