# Question

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 < y < 2;

(d) y ≥ 2. Also find the probability density of Y.

Figure 7.2

(a) y ≤ 0;

(b) 0< y< 1;

(c) 1 < y < 2;

(d) y ≥ 2. Also find the probability density of Y.

Figure 7.2

## Answer to relevant Questions

With reference to Exercise 7.59, what is the probability that the car dealer will receive six inquiries about the 2010 Ford and eight inquiries about the other two cars? In exercise In a newspaper ad, a car dealer lists a ...If X is the number of 7’s obtained when rolling a pair of dice three times, find the probability that Y = X2 will exceed 2. Use the corollary of Theorem 4.15 on page 136 to show that if X1, X2, . . . , Xn constitute a random sample from an infinite population, then cov(Xr – , ) = 0 for r = 1, 2, . . . , n. Theorem 4.15 If the random variables ...Show that the formula for the sample variance can be written as Also, use this formula to recalculate the variance of the sample data of Exercise 8.18. If the range of X is the set of all positive real numbers, show that for k > 0 the probability that √2X – √2v will take on a value less than k equals the probability that X – v / √2v will take on a value less than ...Post your question

0