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)

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) =[tex]E(x)-E(y)=0[/tex]

Var(x-y) =[tex]Var(x)+Var(Y)[/tex]

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

i.e. [tex]Var(x-y) = \frac{35}{12} + \frac{35}{12}[/tex]

Stddev(x-y) =[tex]\sqrt{ \frac{35}{12} + \frac{35}{12}}[/tex]

Hence III option is right

shrutiagrawal1798 shrutiagrawal1798 · Answer 2 · 2021-11-27T10:11:44+01:00

The standard deviation is use to measure the depression of data set with respect to its mean and obtained by the square root of its variance.

The correct option is c.

Given:

The mean of X is [tex]\dfrac{7}{2}[/tex] and variance is [tex]\dfrac{35}{12}[/tex].

Let Y be the random variable.

The X and Y are binomial.

[tex]E(X-Y)=E(X)-E(Y)[/tex]

Write the expression for variance of X and Y.

[tex]Var(X-Y)=Var(X)+Var(Y)[/tex]

Here, x and y are independent cover (x,y) is 0.

Now,

[tex]Var(X-Y)=\dfrac{35}{12}+\dfrac{35}{12}[/tex]

Since the standard deviation is square root of variance.

[tex]S.D=\sqrt{\dfrac{35}{12}+\dfrac{35}{12}}[/tex]

Thus, the correct option is c.

Learn more about what standard deviation is here:

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