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Let X1 and X2 be independent random variables having the

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

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