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SOLVED:Truncated Normal Density. Let x be N(1,1). Using the results in the Appendix, show that: (a) The conditional density f(x / x>1)=2 ϕ(x-1) for x>1 and f(x / x1)=1 2 ϕ(0) and E(x / x1)=var(x / x<1)=1-4 ϕ^2(0). Compare with the unconditional variance of x.
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A truncated discrete distribution is one in which a particular class cannot be observed and is eliminated from the sample space. In particular, if X has a range and the class cannot be observed (as is usually the case), the truncated random variable Xr has a probability density function (pdf) given by P(XT = 2) = 1.2 P(X > 0). Find the probability mass function (pmf), mean, and variance of the O-truncated Poisson(A) random variable.
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