SOLUTION: Please help me solve these problems: Given the probability distribution of a random variable outcome: -2, 4, 10 probability: 0.80, 0.15, 0.05 3. Compute the expected value

Algebra ->  Probability-and-statistics -> SOLUTION: Please help me solve these problems: Given the probability distribution of a random variable outcome: -2, 4, 10 probability: 0.80, 0.15, 0.05 3. Compute the expected value       Log On


   

Question 444189: Please help me solve these problems:
Given the probability distribution of a random variable
outcome: -2, 4, 10
probability: 0.80, 0.15, 0.05
3. Compute the expected value (one digit after decimal point).
4. Compute the variance (two digits after decimal point).
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The expected value of a discrete random variable x is
E%28x%29+=+sum%28+x%5Bi%5Dp%5Bi%5D%2C+i%29 where x%5Bi%5D are the outcomes and p%5Bi%5D are their probabilities
Using the values x = -2, 4, 10; p = 0.8, 0.15, 0.05, we get
E(x) = -2*0.8 + 4*0.15 + 10*0.05 = -0.5
The variance of a discrete random variable x is
sigma%5E2+=+sum%28%28x%5Bi%5D+-+E%28x%29%29%5E2%2Ap%5Bi%5D%2Ci%29
So we have
sigma%5E2 = (-2 - -0.5)^2 + (4 - -0.5)^2 + (10 - -0.5)^2 = 10.35