Mathematics · Probability Distributions
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) = 23
- 2Var(S) = 4
- 3The probability density function of T is fT(t) = t, if 0 < t < 1; 0, otherwise
- 4The probability density function of S is fS(s) = 12e-s/2, if s > 0; 0, otherwise✓
Correct answer
The probability density function of S is fS(s) = 12e-s/2, if s > 0; 0, otherwise
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