Random Variables

I having difficulty with the set up and working of the problem. Let the continuous r.v.X denote the weight (in pounds) of a package. The range of weight of the package is between 45 and 60 pounds. (a) Determine the probability that a package weighs more than 50 pounds. (b) Find the mean and the variance of the weight of packages. HINT: Assume that X is uniformly distributed over (45, 60).

Random Variables

I having difficulty with the set up and working of the problem. The median of a continuous r.v. X is the value of X = Xo such that P(X> or = Xo) = P(X , or = Xo) the mode of X is the value of x = xm at which the pdf of X achieves its maximum value. (a) Find the median and mode of an exponential r.v. X with parameter lambda. (b) Find the median and mode of a normal r.v. X = N ( mu, sigma^2).

Random Variables

I'm having difficulty with the set up and working of the problem. A lot consisting of 100 fuses is inspected by the following procedure: 5 fuses are selected randomly, and if all 5 "blow" at the specified amperage, the lot is accepted. Suppose that the lot contains 10 defective fuses. Find the probabily of accepting the lot. HINT: Let X ba a r.v. equil to the number of defective fuses in the sample of 5 and the result of the r.v. X is known as the "hypergeometric" r.v. with parameters (N,r,n) (a) Find the pmf of X. (b) Find the mean and variance of X.

Random Variables

I'm having difficulty with the set up and working of the problem. A r.v. X is called a Laplace r.v. if its pdf is given by fx(x) = ke ^(-lambda |x|) lambda>0, -infidenity< x < infidenty where k is a constant. (a) Find the value of k. (b) Find the cdf of X. (c) Find the mean and the variance of X.

Random Variables

A carton of 30 lightbulbs includes 5 defective ones. If 4 light bulbs are drawn at random (with out replacement), what is the probability that; (a) 2 of the selected light bulbs are defective. (b) Not all the selected light bulbs are defective.