Question

The random variable X has a probability distribution P(x) of the following form where k is some number:
P(x)={k if x=0 2k if x=1 3k if x=2 0 otherwise
(a)Determine the value of k
(b)Find P(x<2),P(x≤2),P(x≥2)

Answer 1

(a) It is known that the sum of probabilities of a probability distribution of random variables is one.
∴ k + 2k + 3k + 0 = 1

⇒ 6k = 1

⇒ k =$\frac{1}{6}$

(b) P(X < 2) = P(X = 0) + P(X = 1)

=$k+2k=3k=\frac{3}{6}=\frac{1}{2}$

P{X≤2)=P(X=0)+P(X=2)

K+2K+3K=6K=$\frac{6}{6}$

=1

P(X≥2)=P(X=2)+P(X>2)

=3K+0=3K=$\frac{3}{6}$

=$\frac{1}{2}$