Question

If the probability that the random variable X takes the value x is given by 

\(P(X = x) = k(x + 1)3 ^ {- x},\)  x = 0, 1, 2, 3 where k is a constant then \(P(x \geq 3) \) is equal to 

(1) \(\frac{7}{27}\)

(2) \(\frac{8}{27}\)

(3) \(\frac{4}{9}\)

(4) \(\frac{1}{9}\)

Answer 1

Correct option is: (4) \(\frac{1}{9}\)  

\(P(x \geq 3) = 1 - (P(x=0)+P.(x=1)+P(x=2))\)  

\(\Rightarrow 1-\left(k + \frac{2k}{3} + \frac{3k}{3^2}\right)\)  

\(\Rightarrow 1-2k\) 

\(\Rightarrow 1-2 \times \frac{4}{9} = \frac{1}{9}\)