Mathematics · Probability Theory
Let X and Y be independent and identically distributed N(0,1) random variables. Let S = X2 + Y2 and T = e-(X2 + Y2)/2. Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1E(T) = 2/3
- 2Var(S) = 2
- 3The probability density function of T is: fT(t) = 1 if 0 < t < 1, and 0 otherwise
- 4The probability density function of S is: fS(s) = (1/2)e-s/2 if s > 0, and 0 otherwise✓
Correct answer
The probability density function of S is: fS(s) = (1/2)e-s/2 if s > 0, and 0 otherwise
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