Suppose that X follows a poisson distribution with parameter λ=1.416 . P(X≥0)≅?

4. Let X denote the mean of a random sample of size 25 from the distribution whose pdf is f(x) = x²/9,0 < x < 3. Find P(2.21 < X < 2.3). %3D

In the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean  ? = 4.  The profit per foot when the rope is sold is given by X, where  X = 70 − 3Y − Y2.  Find the expected profit per foot.

2.) Use the moment generating function you just proved to verify that for a Poisson distribution, E(X) = λ and Var(X) = λ.

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution.   The per capita consumption of red meat by people in a country in a recent year was normally​ distributed, with a mean of 100 pounds and a standard deviation of 38.6 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined.   ux= o-x= graph=

Suppose that X has a continuous uniform distribution over the interval [1.5, 5.5]. Determine the following: a. Mean, variance, and standard deviation of X b. Р(X < 2.5) c. Cumulative distribution function

3.2.5. Let X have a Poisson distribution with u = 100. Use Chebyshev's inequality to determine a lower bound for P(75 < X < 125). Next, calculate the probability

Its x-12.5 not expone

Suppose that n observations are chosen at random from a continuous pdf fY(y).  What is the probability that the last observation recorded will be the smallest number in the sample?

Let X1 and X2 be IID exponential with parameter  > 0. Determine the distribution ofY = X1=(X1 + X2).