Question

Let x(sub i) be a random variable uniformly distributed over the interval from zero to one, X(sub i)~U(0,1). Let the random variable y be related to X(sub i) as follows: Y Sigma (from i=1 to 108) X(sub i)

Answer 1

\[\sum_{i=1}^{108}X _{i}\]

Answer 2

What is the mean of Y? I have 54. it's the right answer

Answer 3

What is the Variate of Y? i got 972.1666666666666

Answer 4

Is that right?

Answer 5

ah thank god

Answer 6

The mean is definitely right. Write down your logic for Var
\[ Var(Y) = E[(Y-E[Y])^2 \]
= ...

Answer 7

and forget the 108. Write that as n. The particular value is a distraction.

Answer 8

basically just took the summation of (n-m)^2 / n

Answer 9

or rather (ni -m)^2 / n

where i is "sub i"

Answer 10

\[\sum_{i=1}^{n}((n _{i}-\mu)^2)/2\]

Answer 11

er /n

Answer 12

If you are taking a random sample from some distribution with finite variance then

\[Var(Y)=Var\left(\sum_{i=1}^{n}X_i\right)=\sum_{i=1}^{n}Var\left(X_i\right)\]