Question
In: Math
1) The PDF of a Gaussian random variable is given by fx(x). fx(x)= (1/(3*sqrt(2pi) )*e^((x-4)^2)/18 determine...
1) The PDF of a Gaussian random variable is given by fx(x).
fx(x)= (1/(3*sqrt(2pi) )*e^((x-4)^2)/18
determine
a.) P(X > 4) b). P(X > 0). c). P(X < -2).
2) The joint PDF of random variables X and Y is given by
fxy(x,y)=Ke^-(x+y), x>0 , y>0
Determine
a. The constant k.
b. The marginal PDF fX(x).
c. The marginal PDF fY(y).
d. The conditional PDF fX|Y(x|y). Note
fX|Y(x|y) =
fxy(x,y)/fY(y)
e. Are X and Y independent.
Solutions
Expert Solution
2)
Note that for a function to be a pdf, the cumulative distribution in the given domain should sum up to 1. ( i.e. the volume under the given surface function should be = 1)
The last part can also be done using intuition from part d.
We see that the conditional pdf x|y is same as pdf of x. This means that the occurrence of x doesn't depend on y. Therefore they are independent.
milcah answered 4 weeks agoRelated Solutions
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...
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...
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.
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 ).
A random variable Y is a function of random variable X, where y=x^2 and fx(x)=(x+1)/2 from...
A random variable Y is a function of random variable X, where
y=x^2 and fx(x)=(x+1)/2 from -1 to 1 and =0 elsewhere. Determine
fy(y). In this problem, there are two x values for every y value,
which means x=T^-1(y)= +y^0.5 and -y^0.5. Be sure you account for
both of these. Ans: fy(y)=0.5y^-0.5
The random variable X is distributed with pdf fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0....
The random variable X is distributed with pdf
fX(x, θ) = c*x*exp(-(x/θ)2), where x>0
and θ>0.
a) What is the constant c?
b) We consider parameter θ is a number. What is MLE and MOM of
θ? Assume you have an i.i.d. sample. Is MOM unbiased?
c) Please calculate the Crameer-Rao Lower Bound (CRLB). Compare
the variance of MOM with Crameer-Rao Lower Bound (CRLB).
The random variable X is distributed with pdf fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0....
The random variable X is distributed with pdf fX(x,
θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0.
a) Find the distribution of Y = (X1 + ... +
Xn)/n where X1, ..., Xn is an
i.i.d. sample from fX(x, θ). If you can’t find Y, can
you find an approximation of Y when n is large?
b) Find the best estimator, i.e. MVUE, of θ?
The random variable X is distributed with pdf fX(x, θ) = c*x*exp(-(x/θ)2), where x>0 and θ>0....
The random variable X is distributed with pdf
fX(x, θ) = c*x*exp(-(x/θ)2), where x>0
and θ>0. (Please note the equation includes the term
-(x/θ)2 or -(x/θ)^2 if you cannot read that)
a) What is the constant c?
b) We consider parameter θ is a number. What is MLE and MOM of
θ? Assume you have an i.i.d. sample. Is MOM unbiased?
c) Please calculate the Cramer-Rao Lower Bound (CRLB). Compare
the variance of MOM with Crameer-Rao Lower Bound (CRLB).
The probability density function of the continuous random variable X is given by fX (x) =...
The probability density function of the continuous random
variable X is given by
fX (x) = kx, (0 <= x <2)
= k (4-x), (2 <= x <4)
= 0, (otherwise)
1) Find the value of k
2)Find the mean of m
3)Find the Dispersion σ²
4)Find the value of Cumulative distribution function FX(x)
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- What are the 4P's of creativity techniques? Explain the origin of the 4P's. Give some examples...
- Create a program that will take the user through an attempted dungeon escape. The user will...
- A project will generate sales of $46,347 each. The variable costs are $19,519 and the fixed...
- What is SCAMPER creativity technique? How can we apply it to our work? Give some origin...
- I need this in PSEUDO CODE: This looks long, but only because I have to give...
- The cost of external equity capital raised by issuing new common stock (re) is defined as...
- You should consider(NIKE) whether there are any global factors related to the marketing environment in which...
ADVERTISEMENT