Let X be a random variable with the following probability distribution:
Value x of X | P(X=x) |
---|---|
-30 | 0.05 |
-20 | 0.20 |
-10 | 0.05 |
0 | 0.15 |
10 | 0.25 |
20 | 0.30 |
Find the expectation E(X) and variance Var(X) of X. (if necessary, consult a list of formulas.)
E(X) = X * P(X)
= -30 * 0.25 -20 * 0.20 -10 * 0.05 + 0 * 0.15 + 10 * 0.25 + 20 * 0.30
= 2.5
Var(X) = X2 * P(X) - E(X)2
= [ (-30)2 * 0.25 + (-20)2 * 0.20 + (-10)2 * 0.05 + 0 * 0.15 + 102 * 0.25 + 202 * 0.30 ] - 2.52
= 268.75
Let X be a random variable with the following probability distribution:
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