Question

Compute the mean and standard deviation of the random variable

with the given discrete probability distribution.
x P(x)
____________
-3 0.23
-2 0.15
7 0.25
9 0.27
10 0.1

Answer 1

The mean of the random variable is 1.61 and the standard deviation is 5.47.

Step-by-step explanation:

To find the mean of the random variable with the given discrete probability distribution, we multiply each value of the random variable by its corresponding probability and add the products. The formula for the mean is given as E(X) = Σ xP(x). In this case, the mean is calculated as (-3 * 0.23) + (-2 * 0.15) + (1 * 0.25) + (9 * 0.27) + (10 * 0.1) = 1.61.

To find the standard deviation of the distribution, we first find each deviation from the mean, square it, multiply it by its probability, and add the products. The formula for the standard deviation is o = √Σ (x − µ)² P(x). In this case, the standard deviation is calculated as √(((-3 - 1.61)² * 0.23) + ((-2 - 1.61)² * 0.15) + ((1 - 1.61)² * 0.25) + ((9 - 1.61)² * 0.27) + ((10 - 1.61)² * 0.1)) = 5.47.