Final answer:
To find the standard deviation of a discrete random variable X, calculate the variance using the formula Σ (x - µ)² P(x), then take the square root of the variance. For this specific example, the standard deviation of X is approximately 1.63, rounded to two decimal places.
Step-by-step explanation:
To find the standard deviation of a discrete random variable X, we need to calculate the variance first.
The variance is given by the formula Σ (x - µ)² P(x), where Σ denotes the sum over all possible values of X, x is the value of X, µ is the mean, and P(x) is the probability of X taking the value x.
For this specific example, we have the following data:
P(4) = 1/5, P(6) = 2/5, P(8) = 2/5
Substituting the values into the variance formula:
xP(x)(x - µ)² * P(x)41/51.15662/50.14482/51.352
Summing the values in the last column:
1.156 + 0.144 + 1.352 = 2.652
The variance is 2.652. To find the standard deviation, we take the square root of the variance:
√(2.652)≈1.63
So, the standard deviation of X is approximately 1.63, rounded to two decimal places.