Question
In: Statistics and Probability
2. Assume that X has density fX(x) = {cx^2 , if x ∈ [0, 1] 0,...
2. Assume that X has density fX(x) = {cx^2 , if x ∈ [0, 1] 0, otherwise }. Determine the constant c and find the density of Y = 1 − X^2 .
Solutions
orchestra answered 2 years agoRelated Solutions
2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 − x), 0 <...
2. Let X be a continuous random variable with PDF ?fx(x)= cx(1 −
x), 0 < x < 1,
0 elsewhere.
(a) Find the value of c such that fX(x) is indeed a PDF.
(b) Find P(−0.5 < X < 0.3).
(c) Find the median of X.
1. Let X be a random variable with probability density function fX given by fX(x) =...
1. Let X be a random variable with probability density function
fX given by fX(x) = γαγ/ (x + α)^γ+1 , x ≥ 0,
0, x < 0,
where α > 0 and γ > 0.
(a) Find the cumulative distribution function (cdf) FX of X.
(b) Let Y = log(X+α /α) . Find the cdf of Y and identify the
distribution.
(c) How could a realisation of X be generated from an R(0,1)
random number generator?
(d) Let Z...
Let X have the pdf fX(x) = 3(1 − x) 2 , 0 < x <...
Let X have the pdf fX(x) = 3(1 − x) 2 , 0 < x < 1.
(a) Find the pdf of Y = (1 − X) 3 . Specify the distribution of
Y (name and parameter values). (b) Find E(Y ) and Var(Y ).
The (mixed) random variable X has probability density function (pdf) fX (x) given by: fx(x)=0.5δ(x−3)+ {...
The (mixed) random variable X has probability density function
(pdf) fX (x) given by:
fx(x)=0.5δ(x−3)+ { c.(4-x2), 0≤x≤2
0, otherwise
where c is a constant.
(a) Sketch fX (x) and find the constant c.
(b) Find P (X > 1).
(c) Suppose that somebody tells you {X > 1} occurred. Find
the conditional pdf fX|{X>1}(x), the pdf of X given
that {X > 1}.
(d) Find FX(x), the cumulative distribution function of X.
(e) Let Y = X2 . Find...
Given the joint density function of X and Y as fX,Y(x,y) = cx2 + xy/3 0...
Given the joint density function of X and Y as
fX,Y(x,y) = cx2 + xy/3
0 <x <1 and 0 < y < 2.
complete work shading appropriate regions for all integral
calculations.
Find the expected value of Z =
e(s1X+s2Y) where s1 and
s2 are any constants.
1) Let X be a continuous random variable. What is true about fX(x)fX(x)? fX(2) is a...
1) Let X be a continuous random variable. What is true about
fX(x)fX(x)?
fX(2) is a probability.
fX(2) is a set.
It can only take values between 0 and 1 as input.
fX(2) is a number.
2) Let X be a continuous random variable. What is true about
FX(x)FX(x)?
FX(x) is a strictly increasing function.
It decreases to zero as x→∞x→∞.
FX(2) is a probability.
FX(x) can be any real number.
1. Let X be random variable with density p(x) = x/2 for 0 < x<...
1. Let X be random variable with density p(x) = x/2 for 0 < x < 2 and 0 otherwise. Let Y = X^2−2.
a) Compute the CDF and pdf of Y.
b) Compute P(Y >0 | X ≤ 1.8).
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
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