SOLUTION: The probability distribution of a discrete random variable X is shown below x 0 1 2 3 p(x) 0.25 0.40 0.20 0.15 1) Find the expected value of X and the standard deviation of

Algebra ->  Probability-and-statistics -> SOLUTION: The probability distribution of a discrete random variable X is shown below x 0 1 2 3 p(x) 0.25 0.40 0.20 0.15 1) Find the expected value of X and the standard deviation of      Log On


   

Question 381445: The probability distribution of a discrete random variable X is shown below
x 0 1 2 3
p(x) 0.25 0.40 0.20 0.15
1) Find the expected value of X and the standard deviation of X
2) Suppose another random variable, Y = -3X-2. Then find the expected value of Y and the standard deviation of Y
-3X-2)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1) mu+=+0%2A0.25+%2B+1%2A0.40+%2B+2%2A0.20+%2B+3%2A0.15+=+0.40+%2B+0.40+%2B+0.45+=+1.25
.
2) E(-3X-2) = -3E(X) - 2 = -3*1.25-2 = -5.75.
Var%28-3X+-+2%29+=+9Var%28X%29. This means sqrt%28Var%28-3X+-+2%29%29+=+3sqrt%28Var%28X%29%29+=+3sigma. Hence standard deviation of Y = -3X-2 is 3*0.99373 = 2.98119.