# Question: With reference to Exercise 3 102 on page 108 find the

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.

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With 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 ...Post your question