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- The random variable Y is defined by Y = - (X + \X1), where X is another RV. %3D Determine the density and distribution function of Y in terms of those of X. 44If the prob density of a rv is given by f(x)=kx² 0Let Xt = sin(Bt), t>0. Give the distribution of X4. a)If X and Y are two independent uniform distribution with X(0 ,4) and Y(0,6). Find the joint pdf f (x.y). Find P(2.5<X<3.5,1<Y<4)has a 10 chtance of tontainlig a srgame pollutant. Assume that the suuples are andependent Mith regard to the presence of the pollutant. Find the probalility that the next 18 saples (i) exactly 3 contain the pollntant. (ii) at least two samples containm the pollutint. The time takes to repair a particular machine in a factory is a random variable with density function fr(1) = 0. elsewhere fa) Find a. (b) Find the Eumulative distributjon metion and use it to caleulate P(0 < X < I).13 Let X be the standard normal distribution and consider the transformation given by Y = 1/X. Select all answers that apply. Select all answers that apply. Note exp(z) = e^z %D %3D Choose all that apply. O The density of Y is: g(y) = (1/2*pi)^(1/2) * (1/y^2)*exp(-1/(2y^2)) The density of Y is: g(y) = (1/2*pi)^(1/2) *exp(-1/(2y^2)) The values of y for which the density is non zero is y0. The values of y for which the density is non zero is y>0. %3D12Given: image Find the following: show sol. a) Conditional pdf of Y given X=x b) Conditional Expectation of Y given X=x c) Conditional variance of Y given X=xAssume that the weight of hamsters is Normally distributed with μ = 1.2 lbs and σ = 0.25 lbs. Suppose I randomly select 5 hamsters. What is P(X < 1.15)? (Use 3 decimal places)please step by step and thank you!! correct answer, i will make sure to vote!!Let X be uniformly distributed over the interval (-1, 1) and Y be a Bernoulli random variable with parameter p = 0.5. Assume that X and Y are independent of each other. (a) (b) Find and plot the PDF of Z = |X|. Carefully label your plot. Find and plot the PDF of S = X + Y. Carefully label your plot.Let X and Y be independent and normally distributed RVs with the same PDF Find the PDFS of: (i) (ii) x?: (iii) x²+ Y?. X + Y;SEE MORE QUESTIONS