On Sat, 10 May 2008 22:29:44 -0700 (PDT), comsahgh
<hanamanago@[EMAIL PROTECTED]
> wrote:
>Hi
>
>Can anyone help me with this little lot?
>
>
>1.A certain random variable has a probability density function of the
>form
>
>fX(x) = ce?.2xu(x). Find the following:
No, nobody can help you with this, because it's impossible
to tell what the "?" means, and we also don't know what u is.
>(a) the constant c,
>
>(b) Pr(X > 2),
>
>(c) Pr(X < 3),
>
>(d) Pr(X < 3|X > 2).
>
>2.Using the normalization integral for a Gaussian random variable,
>find an
>
>analytical expression for the following integral:
>
>I = ?
>
>??
>exp(?h(ax2 + bx + c)) dx,
>
>where a > 0, b, and c are constants
>
>3. Imagine that you are trapped in a circular room with three doors
>symmetrically
>
>placed around the perimeter. You are told by a mysterious voice
>
>that one door leads to the outside after a two-hour trip through a
>maze.
>
>However, the other two doors lead to mazes that terminate back in the
>room after a two-hour trip, at which time you are unable to tell
>through
>
>which door you exited or entered. What is the average time for escape
>
>to the outside? Can you guess the answer ahead of time? If not, can
>you
>
>provide a physical explanation for the answer you calculate?
>
>
>
>
>4.Let X be a Gaussian random variable with zero mean and arbitrary
>
>variance, ?2. Given the transformation Y = X3, find fY(y).
>
>5.Suppose X is uniformly distributed over (0, 1). Using the results of
>the
>
>previous problem, find transformations Y = g(X) to produce random
>
>variables with the following distributions:
>
>(a) exponential,
>
>(b) Rayleigh,
>
>(c) Cauchy,
>
>(d) geometric,
>
>(e) Poisson.
David C. Ullrich
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