Jana RK, Biswal MP (2006) Genetic based fuzzy goal programming for multiobjective chance constrained programming problems with continuous random variables. Int J Comput Math 83(02):171-179Jana RK, Biswal MP (200
Let XX be a positive continuous random variable. Prove that EX=∫∞0P(X≥x)dxEX=∫0∞P(X≥x)dx.Solution Problem Let X∼Uniform(−π2,π)X∼Uniform(−π2,π) and Y=sin(X)Y=sin(X). Find fY(y)fY(y).Solution
We know that given X=xX=x, the random variable YY is uniformly distributed on [−x,x][−x,x]. Find the joint PDF fXY(x,y)fXY(x,y). Find fY(y)fY(y). Find P(|Y|<X3)P(|Y|<X3).Solution Problem Let XX and YY be two jointly continuous random variables with joint PDF...
Suppose that XX is a continuous random variable whose probability density function is given by f(x)={1x30 if x≥c if x<c.f(x)={1x3 if x≥c0 if x<c. (a) Determine the value of cc. (b) Find the probability P(X>2c)P(X>2c). Read solution Click here if solved 10 Add to...
This is a complex task made more difficult by the fact that the Wiener Process (Brownian Motion) is continuous but has unbounded variation. The first step is to insure that the Stieltjes-form integral with the Wiener Process as integrator actually exists, can be extended to infinite limits, ...
Humans and other animals effortlessly generalize prior knowledge to solve novel problems, by abstracting common structure and mapping it onto new sensorimotor specifics. To investigate how the brain achieves this, in this study, we trained mice on a seri
continuous and (2) weakly (sequentially) closed, that is for any sequence unn∈ℕ⊆Dℱ, xn⇀Xx and ℱxn⇀Yy imply x∈Dℱ and ℱx=y. The Hilbert space X and Y are associated with inner products and norms, ··Xand··Y,||·||Xand||·||Y, respectively. In almost ...
random.randn(m) # Construct the problem. x = cp.Variable(n) objective = cp.Minimize(cp.sum_squares(A @ x - b)) constraints = [0 <= x, x <= 1] prob = cp.Problem(objective, constraints) # The optimal objective is returned by prob.solve(). result = prob.solve() # The ...
(MGF of the Laplace distribution) Let XX be a continuous random variable with the following PDF fX(x)=λ2e−λ|x|.fX(x)=λ2e−λ|x|. Find the MGF of XX, MX(s)MX(s). Problem (MGF of Gamma distribution) Remember that a continuous random variable XX is said to have a Ga...
The problem is subjected to the constraints on shear stress, bending stress, weld length and the buckling load. The four different design variables are the height and the length of the welded joint and thickness and the width of the beam. All the design variables are continuous. The schematic...