Question
Let X be a discrete random variable whose probability distribution is defined as follows:
$\text{P}(\text{X}=\text{x})=\begin{cases}\text{k}(\text{x}+1) & \text{for}\text{ x}= 1,2,3,4\\2\text{kx} & \text{for}\text{ x } =5,6,7\\0&\text{otherwise} \end{cases}$
where k is a constant. Calculate:
$\text{P}(\text{X}=\text{x})=\begin{cases}\text{k}(\text{x}+1) & \text{for}\text{ x}= 1,2,3,4\\2\text{kx} & \text{for}\text{ x } =5,6,7\\0&\text{otherwise} \end{cases}$
where k is a constant. Calculate:
- The value of A if E(X) = 2.94
- Variance of X.
- Standard deviation of X.