Graph the function fx = x^2 + 8x −12 so that the
minimum value is shown,...
Graph the function fx = x^2 + 8x −12 so that the
minimum value is shown, Use the golden section search to find X for
the minimum value of Y (use 6 iterations)
how do you find the (X_low and X_up) for different
functions?
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 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.
a)
Select all solutions of (d^2/dx^2)y(x)+64y(x)=0.
y(x)=3cos(8x)
y(x)=3cos(4x)
y(x)=C1sin(8x)+C2cos(8x)
y(x)=−4sin(8x)
y(x)=C2cos(8x)
b)
Select all solutions of (d^2/dx^2)y(x)+36y(x)=0.
y(x)=C2cos(3x)
y(x)=C1sin(3x)
y(x)=3cos(3x)
y(x)=3cos(6x)
y(x)=3sin(3x)+8cos(3x)
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
Find both the maximum and minimum of the objective function
y − 8x given these constraints. (If an answer
does not exist, enter DNE.)
5x-2y≤13
y≥-4
y-7x≤31
2x+7y≤13