Question

Use the formulas provided below to obtain the same results you determined in Concept Question 3.3.C1 (Determine the mean, variance, and standard deviation of X, the face value of the throw of a fair die.)

Suppose that X is a discrete uniform random variable on the consecutive integers a, a b, for a b. The mean of X is
µ=E(X)=b+a /2
The variance of X is
σ²=(b-a+1)²-1/12
Provide the answers for the variance and standard deviation to 4 decimal places.
Mean =________
Variance =_______
Standard Deviation=__________

Answer 1

The mean, variance, and standard deviation of X, the face value of the throw of a fair die, can be calculated using the formulas provided. For example, if the consecutive integers a and b represent the values of a fair die (a=1, b=6), the mean is 3.5, the variance is 35/12, and the standard deviation is approximately 1.7078.

Step-by-step explanation:

To find the mean, variance, and standard deviation of X, the face value of the throw of a fair die, we can use the formulas provided. The mean, or expected value, of X is given by the formula µ=E(X)=(b+a)/2. The variance of X is given by the formula σ²=(b-a+1)²-1/12.

To obtain the results, you need to substitute the values of a and b into the formulas. For example, if a = 1 and b = 6 (corresponding to a fair die), the mean would be µ=(6+1)/2=3.5, the variance would be σ²=(6-1+1)²-1/12=35/12, and the standard deviation would be √(35/12)≈1.7078 (rounded to 4 decimal places).