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
O other wise
(a) Determine the value of k.
(b) Find P (X <2), P (X s 2), P (X 2)..​

Answer 1

It is known that the sum of probabilities of a probability distribution of random variables is one.

∴k+2k+3k+0=1

⇒6k=1

$</p><p>⇒k = \frac{1}{6}$

(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=1)+P(X=2)

=k+2k+3k

=6k

$= \frac{6}{6}$

= 1

P(X≥2)=P(X=2)+P(X>2)

=3k+0

=3k

$= \frac{3}{6}$

$\huge{ = \frac{1}{2} }$