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quizexe4

# quizexe4 - Solution(a E X = Z ∞-∞ xf x dx = Z 1 x 4 x 3...

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STAT 427 Quiz /Class Exercise 4: With Solution 1. If a discrete random variable X has the pmf P ( X = 3) = 0 . 2 , P ( X = 5) = 0 . 8, find E ( X ). (3 points) Solution: E ( X ) = 3 × P ( X = 3) + 5 × P ( X = 5) = 3 × . 2 + 5 × . 8 = 4 . 6 2. Suppose that X has the pdf f ( x ) = 4 x 3 for 0 x 1 and f ( x ) = 0 otherwise. (a) What is the expected value of X . (4 points) (b) What is the median of X
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Unformatted text preview: Solution: (a) E ( X ) = Z ∞-∞ xf ( x ) dx = Z 1 x 4 x 3 dx = Z 1 4 x 4 dx = 4 5 x 5 | 1 = 4 5 (b) ±or the median x , . 5 = P ( X ≤ x ) = Z x f ( x ) dx = Z x 4 x 3 dx = x 4 | x = x 4 Solve for x , x = 0 . 5 1 / 4 = 0 . 84 1...
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