Here is the full question part:
[100] Suppose you roll two twenty-five-sided dice. Let X1, X2 the outcomes of the rolls of these two fair dice which can be viewed as a random sample of size 2 from a uniform distribution on integers.
List all possible samples and calculate the value of the sample mean (X) and variance (s^2) for each sample?
a) What is the population from which these random samples are drawn?
Find the mean [tex](\mu)[/tex] and variance of this population [tex]( \sigma^2)[/tex]
b) List all possible samples and calculate the value of the sample mean (X) and variance (s^2) for each sample?
Answer:
a) mean [tex](\mu)[/tex] = 13
variance of this population [tex]( \sigma^2)[/tex] = 52
b) a table is make in a document file attach below show all the possible samples with their corresponding calculation of the sample mean (X) and their corresponding variance [tex]( \sigma^2)[/tex] for each sample
Step-by-step explanation:
a)
A random sample of 2 is collected from : P (X = x) = [tex]\frac{1}{25}[/tex] ;
where x = 1,2,3 ... , 25 = 0 otherwise
[tex]\mu = \sum (x)[/tex]
[tex]\sum ^{25}_{x=1} \frac{x}{25}[/tex] = [tex]\frac{1}{2}*\frac{25*26}{2}[/tex]
= 13
[tex]\sum (X^2) = \sum^{25}_{x=1} = \frac{1}{25} *\frac{25*26*51}{26}[/tex]
= 13 × 17
[tex]\sigma^2 = Var (X)[/tex]
[tex]\sigma^2 =\sum (X^2) - \sum ^2X[/tex]
= 13 × 4
= 52
b) The document below clearly depicts the lists of all the possible samples with their calculated value of the sample mean (X) and variance [tex]( \sigma^2)[/tex] for each sample.
