The probability density function of the discrete random variable $X$ is given by \[P(X=x)=a\left(\

Question

The probability density function of the discrete random variable $X$ is given by $$P(X=x)=a\left(\frac{3}{4}\right)^x \text{ for}\hspace{0.5em} x=0,1,2,...$$ Find the value of the constant $a$. Find the values of $P(X<3)$ and $P(X>2)$.

Accepted Answer

(i) $ \frac{1}{4} $; (ii) $ \frac{37}{64}$, $\frac{27}{64} $

Finding unknown constant in a probability distribution function

Finding unknown constant in a probability distribution function