Question

The probability distribution function of a discrete random variable X is
f(x) = `{{:(2k",",  x = 1),(3k",",  x = 3),(4k",", x = 5),(0",",  "otherwise"):}`
where k is some constant. Find k 

Answer 1

Let X be the random variable of a probability distribution function

W.K.T `sum"pi"` = 1

P(x = 1) + P(x = 3) + P(x = 5) = 1

2k + 3k + 4k = 1

9k – 1

⇒ k = 1/9