Question

Suppose that has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard deviation of the random variable .

Answer 1

Answer:

The question is incomplete, complete question is:

Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard deviation of the random variable Y = 5X and compare to the corresponding results for X.

Answer:

Mean: 22.5

Variance: 206.25

Standard Deviation: 14.36

Step-by-step explanation:

See the attached picture for explanation.

Answer 2

The question is incomplete and the complete question is;

Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard deviation of the random variable Y = 5X and compare to the corresponding results for X.

Answer:

For random variable X;

Mean = 4.5

Variance = 8.25

Standard deviation = 2.87

For random variable 5X;

Mean = 22.5

Variance = 206.25

Standard Deviation = 14.36

Comparing these values of variable 5X to variable X, we can say the following ;

- The mean of variable 5X is five times the mean of Variable X

- The variance of variable 5X is 25 times the variance of variable X.

- The standard deviation of variable 5X is five times the standard deviation of Variable X

Step-by-step explanation:

From the question, the random variable X has the parameters of;

a=0 and b=9

Thus for the mean; E(X) = (0+9)/2 = 9/2 = 4.5

Variance;

Thus Var(X) = [(9 + 0 + 1)² - 1]/12 = 99/12 = 8.25

We know that;

standard deviation = √(Var(X))

Thus, Standard deviation = √(8.25) = 2.87

Now let's do the same for the random variable 5X;

E(5X) = 5 x (E(X) = 5 x 4.5 = 22.5

Var(5X) = E[(5X - E(5X))²]

Factorizing out 5,we get

Var(5X) = 5² x E [(X - E(X))²]

Thus Var(5X) = 25 x Var(X) = 25 x 8.25 = 206.25

Standard deviation of random variable 5X = √Var(5X) = √206.25 = 14.36