Question

Let X be a random variable whose values are the number of dots that appear on the uppermost face when a fair die is rolled. The possible values of X are 1, 2, 3, 4, 5, and 6. The mean of X is 7/2 and the variance of X is 35/12. Let Y be the random variable whose value is the difference (first minus second) between the number of dots that appear on the uppermost face for the first and second rolls of a fair die that is rolled twice. What is the standard deviation of Y
a. √(35/12)
b. √(35/12) + √(35/12)
c. √{(35/12) + (35/12)}
d. √(35/12) - √(35/12)

Answer 1

Answer:

Hence III option is right

Step-by-step explanation:

Given that X is a random variable whose values are the number of dots that appear on the uppermost face when a fair die is rolled. The possible values of X are 1, 2, 3, 4, 5, and 6.

Let X be the reading on I dieand Y on IIdie

Both Xand Y are binomial

Given that  The mean of X is 7/2 and the variance of X is 35/12.

E(X_y) =$E(x)-E(y)=0$

Var(x-y) =$Var(x)+Var(Y)$

(Since x and y are independent covar (x,y) is 0)

i.e. $Var(x-y) = \frac{35}{12} + \frac{35}{12}$

Stddev(x-y) =$\sqrt{ \frac{35}{12} + \frac{35}{12}}$

Hence III option is right