Answer:
In order to find the variance we need to find first the second moment given by:
And replacing we got:
The variance is calculated with this formula:
And the standard deviation is just the square root of the variance and we got:
Step-by-step explanation:
Previous concepts
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
Solution to the problem
LEt X the random variable who represent the number of defective transistors. For this case we have the following probability distribution for X
X 0 1 2 3
P(X) 0.92 0.03 0.03 0.02
We can calculate the expected value with the following formula:
And replacing we got:
In order to find the variance we need to find first the second moment given by:
And replacing we got:
The variance is calculated with this formula:
And the standard deviation is just the square root of the variance and we got: