Asked by RVE
FUNCTIONS OF A STANDARD NORMAL
The random variable X has a standard normal distribution. Find the PDF of the random variable Y, where:
1. Y=3X-1 , Y = 3X - 1
answer:
fY(y)=1/3*fX*(y+1/3)
f_ Y(y)=1/3*f_ X*(y+1/3)
2. Y=3X^2-1. For y>=-1,
Y = 3X^2 - 1. For y >= -1,
answer:
fY(y)=1/3*sqrt(3/y+1)*fX*sqrt(y+1/3)
f_Y(y)=1/3*sqrt(3/y+1)*f_X*sqrt(y+1/3)
(no need to answer. Public interest problem)
The random variable X has a standard normal distribution. Find the PDF of the random variable Y, where:
1. Y=3X-1 , Y = 3X - 1
answer:
fY(y)=1/3*fX*(y+1/3)
f_ Y(y)=1/3*f_ X*(y+1/3)
2. Y=3X^2-1. For y>=-1,
Y = 3X^2 - 1. For y >= -1,
answer:
fY(y)=1/3*sqrt(3/y+1)*fX*sqrt(y+1/3)
f_Y(y)=1/3*sqrt(3/y+1)*f_X*sqrt(y+1/3)
(no need to answer. Public interest problem)
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