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Unformatted text preview: density fሺx ଵ , x ଶ ሻ ൌ ൜ 4x ଵ x ଶ , 0 ൏ x ଵ ൏ 1, 0 ൏ x ଶ ൏ 1 0, elsewhere . Let Y ଵ ൌ X ଵ ଶ and Y ଶ ൌ X ଵ X ଶ . (1) Find the joint probability density of Y ଵ and Y ଶ . (2) Let A ൌ ሼሺx ଵ , x ଶ ሻ|0 ൏ x ଵ ൏ 1, 0 ൏ x ଶ ൏ 1ሽ . Draw a picture of the mapping of A. 5. Show that if X is a random variable having the Poisson distribution with the parameter λ and λ ื ∞ , then the moment ‐ generating function of Z ൌ ±ି √ approaches the moment ‐ generating function of the standard normal distribution. 6. If Z is a standard normal random variable, find the probability density function of X ൌ Z ଶ ....
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This note was uploaded on 05/09/2011 for the course DIF 1486 taught by Professor Yow-jenjou during the Spring '11 term at National Chiao Tung University.
- Spring '11