# Question: Suppose and are independent discrete random variables Find the PMF

Suppose and are independent discrete random variables. Find the PMF of L = M + N for each of the following cases: (a) and both follow a uniform distribution,

(a) M and N both follow a uniform distribution,

PM (k) = PN (k) = 1/K, k = 0, 1, 2… K–1.

(b) M and N follow different geometric distributions,

PM (m) = (1–p) pm , m = 0, 1, 2….

Pn (n) = (1–q) qn , m = 0, 1, 2….

(c) M and N both follow the same geometric distribution,

PM (m) = PN (m) = (1–p) pm, m = 0, 1, 2…

(a) M and N both follow a uniform distribution,

PM (k) = PN (k) = 1/K, k = 0, 1, 2… K–1.

(b) M and N follow different geometric distributions,

PM (m) = (1–p) pm , m = 0, 1, 2….

Pn (n) = (1–q) qn , m = 0, 1, 2….

(c) M and N both follow the same geometric distribution,

PM (m) = PN (m) = (1–p) pm, m = 0, 1, 2…

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