A random variable X has the following probability distribution:Determine (i) k (ii) `P(X<3)`(iii) `P(X >6)` (iv) `P(0

Explanation

To solve the problem step by step, we will follow the instructions given in the video transcript and break down each part of the question.

### Given Probability Distribution
Let the random variable \( X \) take values from \( 0 \) to \( 7 \) with the following probabilities:
- \( P(X=0) = k \)
- \( P(X=1) = 2k \)
- \( P(X=2) = 2k \)
- \( P(X=3) = 3k \)
...