Question

# Please solve the following showing all the steps. Using the sample mean, variance, and standard deviation...

Please solve the following showing all the steps.
Using the sample mean, variance, and standard deviation equations with steps. I don't know how to do this and would like to learn.

Also, is this considered a loaded dice?

Consider the roll of two dice. Let X be a random variable representing the sum of the number of dots appearing on each of the dice. The probabilities of each possible value of X are as follows:

 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36

Determine the expected value and standard deviation of X.

Sol:

Expected value of X =2*(1/36)+3*(2/36)+4*(3/36)+5*(4/36)+6*(5/36)+7*(6/36)+8*(5/36)+9*(4/36)+10*(3/36)+11*(2/36)+12*(1/36)

E(X)=7

expected value=7

Variance of X= =2^2*(1/36)+3^2*(2/36)+4^2*(3/36)+5^2*(4/36)+6^2*(5/36)+7^2*(6/36)+8^2*(5/36)+9^2*(4/36)+10^2*(3/36)+11^2*(2/36)+12^2*(1/36)-(7)^2

=54.83333-49

= 5.83333

standard deviation of x=sqrt(variance)=sqrt(5.83333)= 2.415229

expected value=7

standard deviation of X.=2.415229

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