Question

measurement error that is continuous and uniformly distributed from millivolts is added to the true voltage of a circuit. then the measurement is rounded to the nearest millivolt so that it becomes discrete. suppose that the true voltage is 219 millivolts. what is the mean and variance of the measured voltage

Answer 1

Question has missing details (Full question below)

Measurement error that is continuous and uniformly distributed from –3 to +3 millivolts is added to a circuit’s true voltage. Then the measurement is rounded to the nearest millivolt so that it becomes discrete. Suppose that the true voltage is 219 millivolts. What is the mean and variance of the measured voltage

Answer:

Mean = 219

Variance = 4

Explanation:

Given

Let X be a random variable measurement error.

X has a discrete uniform distribution as follows

a = 219 - 3 = 216

b = 219 + 3 = 222

Mean or Expected value is calculated as follows;

E(x) = ½(216+222)

E(x) = ½ * 438

E(x) = 219

Variance is calculated as follows;

Var(x) = ((b-a+1)²-1)/12

Var(x) = ((222-216+1)²-1)/12

Var(x) = (7²-1)/12

Var(x) = 48/12

Var(x) = 4