Dear Professors/Instructors,

Could you please explain the principle behind the solution to problem 8 in Week-8 (i.e. 1. How many more runs does Sachin score on average after having scored x runs). The assumption made is not very convincing.

```
x_arr = np.arange(0, 101, 5) #[0, 5, ....100]
indices = sachin >= x_arr #build 21x225 table
```

As I understand, what is being done is an `indices table`

is built. Further for x (leâ€™ts say x=5), indicesâ€™ 1st row will have an array of 225 elements where element will be True if the score is >= 5, False otherwise.

(similarly x=0 will correspond to indicesâ€™ 0th row, and x=100 will correspond to indicesâ€™ 20th row.)

Once the table is there, 1) you can pick a indices row (depending on `x`

value) and 2) use it as a index in `sachin`

to pick up relevant scores (more runs than 0, 5, 10â€¦ etc), 3)calculate `more runs than x`

by subtracting x and 4) finally take the mean.

Which assumption?

The assumption that â€śonce he crosses that barrier of scoring few runs when x=5, his number of runs that will likely add to his score would be greater than his averageâ€ť - is what I am not understanding.

Is this a proposition? Or rather how do we or to say to what confidence level we can say this inside the quotes to be true?

Ok, I think i understand your question better, but I donâ€™t have a good answer. Here is my understanding:

- Question: How many more runs Sachin score on average after having scored x runs?

As the solution approach shown in videos, this question is not about making a hypothesis (that Sachin scores so many runs if â€¦) whose acceptance/rejection will need some likelihood/confidence level calculation. Its simple calculating average score Sachin scores/scored after passing x runs from the given innings/data (which is deterministic, no probability or likelihood involved).

Having said that, I kind of agree you can debate about how question is phrased.

Lastly, if this question had to be seen as having a sample data given and making a prediction about population (innings spanning his all career) parameters with some confidence level, what would be your Null Hypothesis and sample statistics (this material is covered in week 20)?

Ok @sanjayk. I could understand your reformulation statement of the question now (â€ścalculating average score Sachin scores/scored after passing x runs from the given innings/dataâ€ť). It becomes more clear with the meaning now.

Though I could not do this part myself, and I had to take the video help of Prof Pratyush, I will again attempt with my understanding now as it is clearer.

Thanks a lot