Answer: To find the standard deviation of a probability distribution, we need to first calculate the mean or expected value of the distribution, which is given by:
E(X) = Σ [xi * P(xi)]
where xi is the ith outcome and P(xi) is its probability.
So, for the given distribution:
E(X) = (0 * 0.1) + (1 * 0.05) + (2 * 0.1) + (3 * 0.75) = 2.4
Next, we need to calculate the variance of the distribution, which is given by:
Var(X) = Σ [(xi - E(X))^2 * P(xi)]
So, for the given distribution:
Var(X) = (0 - 2.4)^2 * 0.1 + (1 - 2.4)^2 * 0.05 + (2 - 2.4)^2 * 0.1 + (3 - 2.4)^2 * 0.75 = 0.69
Finally, the standard deviation of the distribution is the square root of the variance:
SD(X) = sqrt(Var(X)) = sqrt(0.69) ≈ 0.83
Therefore, the standard deviation of this probability distribution is approximately 0.83, rounded to 2 decimal places.
Explanation: