Question

X =	1	2	3	4	5
P(X =)	$\frac{1}{2}$	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{16}$	P

The probability distribution of a random variable X taking values 1, 2, 3, 4, 5 is given
(a) Find the value of P.
(b) Find the mean of X.
(c) Find the variance of X.

Answer 1

${\sum }_{i=1}^{5}P(X=i)=1$

$\Rightarrow P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=1$

$\Rightarrow \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+P=1$

$\Rightarrow P=1-\frac{1}{16}$

$\Rightarrow P=\frac{15}{16}$

Mean of $X=\frac{1+2+3+4+5}{5}=3$

Variance of $X=\frac{{(1-3)}^2+{(2-3)}^2+{(3-3)}^2+{(4-3)}^2+{(5-3)}^2}{4}=\frac{4+1+1+4}{4}=\frac{5}{2}$