- Let Y = 2X^2 + 1, where x is exponential random variables. Fin —- a). P[0<=Y<=5] —–b). PDF of Y. (using functions of random variable).
- PDF of a random variable X is given by F(x) = {c(1-x)^4 -1<=x<=1 , 0 else where } — a). Find c —b). find cdf of x —c). find p[|x|<0.5]
- a). Find variance of Geometric random variables using characteristic function. —b). Let X be a binomial random variables that results form performance of n Bernoulli trials with probability of success p. Suppose that x=2. show that probability of success in jth and kth trials is given by i.e P[(x=j) ⋂ (x=k)] = (s-p)^j+k-1 p^2.
- Joint pdf of random variables X and Y is given by fx,y(x,y) = { 2e^-x e^-y, 0 elsewhere} .. —a). Find correlation of X and Y i.e E[XY] —b). Find COV(X,Y).
- A system has three identical components and the system is functioning if two or more components are functioning. —a). Find the reliability and MTTF of the system if the components lifetimes are exponential random variables with mean 1. —b). find the reliability of the system if one of the components has mean 2.
Exam LaLa 