The probability distribution of a random variable `X` is given as under: `P(X=x)={k x^2forx=1,2,3 2k xforx=4,5,6 0ot h e r w i s e` , where `k` is a constant. Find (i) `P(Xgeq4` ) (ii) `E(X)` (iii) `E(3X^2)`

Explanation

To solve the problem step by step, we will follow the instructions provided in the video transcript.

### Step 1: Define the Probability Distribution
The probability distribution of the random variable \( X \) is given as:
\[
P(X=x) =
\begin{cases}
k x^2 & \text{for } x = 1, 2, 3 \\
...