SOLUTION: Suppose that the random variable Y has probability distribution given by: y p(y) -2 0.11 0 0.32 3 0.57 Find the mean, variance, and standard deviation of Y .

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that the random variable Y has probability distribution given by: y p(y) -2 0.11 0 0.32 3 0.57 Find the mean, variance, and standard deviation of Y .       Log On


   



Question 1034553: Suppose that the random variable Y has probability distribution given by:

y p(y)
-2 0.11
0 0.32
3 0.57
Find the mean, variance, and standard deviation of Y .
μ Y =
σ 2 Y =
σ Y =
What is the probability that Y is between μ Y −3σ Y and μ Y +3σ Y ? You may find it helpful to draw a probability histogram and mark μ Y , μ Y −3σ Y , and μ Y +3σ Y .
P(μ Y −3σ Y

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
E%28Y%29+=+mu%5BY%5D+=+-2%2A0.11+%2B+0%2A0.32+%2B+3%2A0.57++=+1.49.
Now E%28Y%5E2%29+=+%28-2%29%5E2%2A0.11+%2B+0%5E2%2A0.32+%2B+3%5E2%2A0.57++=+5.57
%28sigma%29%5E2%5BY%5D+=+E%28Y%5E2%29+-++%28mu%5BY%5D%29%5E2+=+5.57+-+1.49%5E2+=+3.3499
==> sigma%5BY%5D+=+sqrt%283.3499%29+=+1.83, to three significant figures