esmeraldavelez63
14.04.2020 •
Mathematics
Assume X and Y are random variables with both have mean 3 and variance 2. Calculate E left square bracket X squared plus 4 Y minus 5 right square bracket. (Hint: Think how to calculateE left square bracket X squared right square bracket given the mean and the variance).
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Ответ:
E[X² + 4Y - 5] = 18
Step-by-step explanation:
Mean = E(X) = 3
E(Y) = 3
Variance = Var(X) = 2
Var(Y) = 2
Calculate E[X² + 4Y - 5]
E[X² + 4Y - 5] = E(X²) + 4E(Y) - E(5)
But Var(X) = E(X²) - [E(X)]²
E(X²) = Var(X) + [E(X)]² = 2 + 3² = 2 + 9 = 11
E(5) = 5
E[X² + 4Y - 5] = E(X²) + 4E(Y) - E(5) = 11 + 4(3) - 5 = 11 + 12 - 5 = 18
Hope this Helps!!!
Ответ: