Question

The standard deviation of a random variable X is 2.3 and a random variable Y is 1.2.X and Y are independent random variables. Then, the standard deviation of the random variable (X+Y) is 3.5 . Is the statement True or False?

a) True
b) False

Answer 1

The claim that the standard deviation of the sum of two independent random variables X and Y is 3.5, given their individual standard deviations are 2.3 and 1.2, respectively, is false. The correct standard deviation of (X+Y) is approximately 2.6.

Step-by-step explanation:

The statement about the standard deviation of the random variable (X+Y) being 3.5 given that the standard deviations of X and Y are 2.3 and 1.2, respectively, is False.

Since X and Y are independent random variables, we use the following formula to find the standard deviation of the sum of X and Y:

σX+Y = √(σX2 + σY2)

Substituting the given standard deviations into the formula:

σX+Y = √(2.32 + 1.22)

σX+Y = √(5.29 + 1.44)

σX+Y = √6.73

σX+Y = 2.5945 approximately

Thus, the correct standard deviation of (X+Y) is about 2.6, not 3.5.