FRM Part I · FRM Exam Part I · Common Univariate Random Variables
If U is a standard continuous uniform random variable on [0, 1], which transformation correctly generates a continuous uniform variable on [5, 9]?
The correct transformation is 5 + 4U. Scaling U by the interval width, 9 minus 5 equals 4, and shifting by the lower bound 5 maps [0, 1] onto [5, 9]. The other expressions produce ranges with wrong endpoints.
- A5 + 9U
- B4 + 5U
- C9 - 5U
- D5 + 4UCorrect
Explanation
A uniform on [a, b] is a + (b-a)U = 5 + 4U, ranging from 5 to 9. 5 + 9U ranges to 14; 4 + 5U ranges 4 to 9; 9 - 5U ranges 4 to 9.
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