In the probability and statistics theory, the Poisson distribution is a discrete probability distribution and has only one parameter known as scale parameter or mean parameter. The mean and variance of the distribution are equal to the parameter....
Let X be an exponentially distributed random variable with parameter lambda = 1 / 2. Determine the probability distribution function of the random variable Y = X / 2. What kind of distribution does Y have? a. Exponential with parameter lambda = 1 /...
Let X be a random variable distributed with probability density function f(x)= 0.1e^{-0.1x}, 0 \leq x < \infty , i.e, X is the exponential random variable with parameter 0.1. Then E(X) = \frac {1}{0.1} = 10. Suppose that X has the Binomial(n, p) distribution. Find the ...
Let X and Y be independent random variables having the exponential distribution, E(X) = 1/lambda and E(Y) = 1/mu, Find the joint probability density function of min(X.Y) and max(X,Y) - min(X,Y). Suppose that three random variable X...
Let Y_1, Y_2,..., Y_n denote a random sample from a population with mean \mu and variance \sigma^2. Consider the following three estimators for \mu: \hat \mu_1= \frac{1}{2} (Y_1 +Y_2), \hat \mu_2=\frac{1}{4}Y_1 +\frac{Y_2+\Lambda +Y_(n-1)}{2(n-2)}+...
(a) A cubic crystal shows a diffraction maximum form copper radiation, \lambda=1.54 and \theta=33°, corresponding to diffraction from (130). Calculate the lattice parameter. (b) Calculate t Develop the equation of motion in terms of the variable x for the...
The probability density function, in statistics, is the function through which probabilities of the continuous random variables are computed by an integrating it. It must be positive for all the ranges as it is a probability distribution.Answer...
Y_1, Y_2, cdots converges in probability to the degenerate r.v. Y where P(Y=thata) =1. Let X_1,,..., X_n be a random sample from f(x|theta) = theta x^{theta - 1} Assume that the prior distribution of Theta is given by g_{Theta}(...
a) Demonstrate that f(x; lambda) is a probability distribution. (Hint: What are the properties of a probability distribution?) b) Solve for the cumulative distribution function (CDF) for the exponenti Let X be a probability distribution over [0,1], with a density f...
Let X and Y be independent exponential random variables with parameter. Calculate P(X + Y less than or equal to lambda^-1). Consider a normal random variable ''X'' with \bar{x} = 60, \; s = 6. Give the probability that X is at most 78....