# Category: Statistics

## Using GC to calculate Expectation and Variance of Discrete Random Variable

**Example 1**

**Solution**

Enter the data in the GC as follows:

Variance can also calculated using the GC as follows:

**Example 2**

RI 2018 J2 MYE Q13i

## Assumptions for binomial distribution

In 2013 alevel examiner’s report, it was mentioned that only a minority of candidates were successful in giving both assumptions about the binomial distribution.

**9740 N2013/II/7**

**Solution**

## Common errors in hypothesis testing

This marker’s report from DHS 2016 JC2 mid year exam highlight the common errors in hypothesis testing.

## Distinguish X1+X2 from 2X

This challenging question on normal distribution was posted in Edusnap by a student.

There were two mistakes made:

1) Interpreting the distribution of 2 large hampers and n small hampers as 2L + nS.

2) Calculation of variance

Here is the correct solution:

Smallest possible value of n = 9

————————-

When the question mentions n items, the distribution is X1+X2+…Xn. When the question asks for “n times of a randomly chosen..”, then the distribution is nX.

Students also need to be familiar with calculating the expectation and variance of the sum or difference of normal distribution using the formula:

## Challenging Normal Distribution problem 3

## Calculating Mean and Variance of coded data

## Understanding Hypothesis Testing

The concept behind hypothesis testing is that assuming the null hypothesis is true, what is the probability of getting the sample results. If the probability is very low such as 5%, we reject the null hypothesis as the sample results is unlikely to occur due to random chance when assuming the null hypothesis is true. In H2 math, the test statistic is often based on normal or T distribution. However, the same principle can be applied for other distributions.

**Example from RI Tutorial Section C (Challenging Questions)**