Question

In: Statistics and Probability

Find the joint pdf of the random sampleY1,...,Yn from the following distributions: a. Poisson(λ). b.N(0,σ^2).

Find the joint pdf of the random sampleY1,...,Yn from the following distributions:

a. Poisson(λ).

b.N(0,σ^2).

Solutions

Expert Solution

PIC:Joint pdf's for samples drawn from Poisson and Normal distribution.


Related Solutions

(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf...
(i) Find the marginal probability distributions for the random variables X1 and X2 with joint pdf                     f(x1, x2) = 12x1x2(1-x2) , 0 < x1 <1   0 < x2 < 1 , otherwise             (ii) Calculate E(X1) and E(X2)     (iii) Are the variables X1 ­and X2 stochastically independent? (iv) Given the variables in the question, find the conditional p.d.f. of X1 given 0<x2< ½ and the conditional expectation E[X1|0<x2< ½ ].
The random variables ? and ? have the following joint pdf. ??,? (?, ?) = ??...
The random variables ? and ? have the following joint pdf. ??,? (?, ?) = ?? -8x^2-18y^2 a) Find the mean and variance of ? and ? and the value of ?. b) Determine if ? and ? are independent. c) Determine the distribution of ? and ?.
(1 point) Let ?1 and ?2 have Poisson distributions with the same average rate λ =...
(1 point) Let ?1 and ?2 have Poisson distributions with the same average rate λ = 0.6 on independent time intervals of length 1 and 3 respectively. Find Prob(?1+?2=3) to at least 6 decimal places.
Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...
Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find  P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]
Show that the skewness of X~Poisson(λ) is λ^-(1/2)
Show that the skewness of X~Poisson(λ) is λ^-(1/2)
Using binomial and poisson distributions to find probabilities using the two equations from binominal and poisson...
Using binomial and poisson distributions to find probabilities using the two equations from binominal and poisson An inspector looks for blemishes in the finish on porcelain and counts the number of defects on batches of 12 vases. If the mean is 1.2, what is the probability he finds exactly one blemish? (poisson) A nail salon tracks the number of customers that enter each minute. In an average minutes 0.35 customers enter. What is the probability at least 1 customer enters...
Let X1,...,Xn be exponentially distributed independent random variables with parameter λ. (a) Find the pdf of...
Let X1,...,Xn be exponentially distributed independent random variables with parameter λ. (a) Find the pdf of Yn= max{X1,...,Xn}. (b) Find E[Yn]. (c) Find the median of Yn. (d) What is the mean for n= 1, n= 2, n= 3? What happens as n→∞? Explain why.
(a) Let X and Y have the joint pdf ???(?, ?)=1, 0≤x≤3/2, 0≤y≤1, zero elsewhere. Find:...
(a) Let X and Y have the joint pdf ???(?, ?)=1, 0≤x≤3/2, 0≤y≤1, zero elsewhere. Find: 1 The pdf of Z=X+Y 2 The pdf of Z=X.Y
Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0.  elsewhere (a) Find the...
Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0.  elsewhere (a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1. (b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1. (c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2). (d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).
Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x <...
Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x < infinity and 0 < y < infinity with parameters λ > 0 and μ > 0 a) Find c such that this is a PDF. b) Show that X and Y are Independent c) What is P(1 < X < 2, 0 < Y < 5) ? Leave in exponential form d) Find the marginal distribution of Y, f(y) e) Find E(Y)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT