Let X be a discrete random variable with pmf p(n) = (n−1)(0.4)2(0.6)n−2, n ≥ 2 and...

Question

Question

Let X be a discrete random variable with pmf p(n) = (n−1)(0.4)2(0.6)n−2, n ≥ 2 and 0 otherwise. Find the mode of X

Answer 1

Answer #1

Here

p(n) = (n-1) 0.4² 0.6^n-2 , n >= 2

so here we have to find the mode of X

so here the mode of X would be the for which the value of p(n) would be highest.

Here for n =2

p(2) = (2-1) (0.4)² (0.6)⁰= 0.16

for n = 3

p(3) = (3-1) (0.4)² (0.6)¹= 0.192

for n = 4

p(4) = (4-1) (0.4)² (0.6)²= 0.1728

for n = 5

p(5) = (5-1) (0.4)² (0.6)³= 0.13824

so here from now on it will diminish so here for x = 3, p(n) would be highest so here mode of the distribution is 3.

Answer 2

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