1. ## Chebishev

1)
a dice is being rolled 360 times. the dice has 1 red side and 5 black. what is the upper bound to the probability of falling on a red side more than 41 times and less than 59 times ?

2)

X - counts how many times the dice was red, up to 36 times
Y - counts how many times the dice was red up to 50 times
find COV(X,Y)

thanks a million !

2. isn't there something wrong with the data ???

3. Originally Posted by WeeG
1)
a dice is being rolled 360 times. the dice has 1 red side and 5 black. what is the upper bound to the probability of falling on a red side more than 41 times and less than 59 times ?
The mean number of reds on a single roll of a die is $\displaystyle \mu_1=1/6$, the SD is:

$\displaystyle \sigma^2_1=(1/6)(1-1/6)^2+(5/6)(0-1/6)^2=5/6$

In $\displaystyle 360$ rolls the mean number of reds is $\displaystyle \mu=360 \mu_1=60$ and the standard deviation is $\displaystyle \sigma=\sigma_1/\sqrt{360}$

Now if the range for the number of reds were $\displaystyle 51$ to $\displaystyle 69$ this would now be a straight forward application of Chebyscev's inequality (or if the number of throws were $\displaystyle 300$ rather than $\displaystyle 360$).

I don't think that the 1-sided Chebyshev inequality will work here, so you may have a type.

CB