suppose x is a uniform random variable with c=40 and d=70. find the standard deviation of x
To find the standard deviation of a uniform random variable, you can use the formula:
Standard Deviation = (d - c) / √12
where "c" is the lower bound of the uniform random variable and "d" is the upper bound.
In this case, the lower bound (c) is 40 and the upper bound (d) is 70.
So, the standard deviation of x is:
Standard Deviation = (70 - 40) / √12
Standard Deviation = 30 / √12
Calculating the value of √12:
√12 ≈ 3.4641
Substituting the value:
Standard Deviation ≈ 30 / 3.4641
Standard Deviation ≈ 8.6603
Therefore, the standard deviation of x is approximately 8.6603.
To find the standard deviation of a continuous uniform random variable, you can use the following formula:
Standard Deviation (σ) = (b - a) / √12
Where:
- 'a' is the lower bound of the uniform distribution (in this case, a = 40)
- 'b' is the upper bound of the uniform distribution (in this case, b = 70)
Let's substitute these values into the formula:
σ = (70 - 40) / √12
Now, we need to simplify the expression:
σ = 30 / √12
To calculate the square root of 12, we divide the square root of 12 by the square root of 12:
σ ≈ 30 / √(4 × 3)
Next, we simplify the expression further:
σ ≈ 30 / (√4 × √3)
σ ≈ 30 / (2 × √3)
Finally, we calculate the value:
σ ≈ 30 / (2 × 1.732)
σ ≈ 30 / 3.464
σ ≈ 8.660
Therefore, the standard deviation of the uniform random variable x with c = 40 and d = 70 is approximately 8.660.