Question

Suppose X and Y are independent Poisson random variables with respective parameters λ = 1 and...

Suppose X and Y are independent Poisson random variables with respective parameters λ = 1 and λ = 2. Find the conditional distribution of X, given that X + Y = 5. What distribution is this?

Homework Answers

Answer #1
  • Please check attachment  

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X and Y be independent random variables following Poisson distributions, each with parameter λ =...
Let X and Y be independent random variables following Poisson distributions, each with parameter λ = 1. Show that the distribution of Z = X + Y is Poisson with parameter λ = 2. using convolution formula
Let X and Y be independent exponential random variables with respective parameters 2 and 3. a)....
Let X and Y be independent exponential random variables with respective parameters 2 and 3. a). Find the cdf and density of Z = X/Y . b). Compute P(X < Y ). c). Find the cdf and density of W = min{X,Y }.
Suppose X, T are independent exponential random variables with parameters λX and λT . Find the...
Suppose X, T are independent exponential random variables with parameters λX and λT . Find the conditional density of X given X < T .
Let X follow Poisson distribution with λ = a and Y follow Poisson distribution with λ...
Let X follow Poisson distribution with λ = a and Y follow Poisson distribution with λ = b. X and Y are independent. Define a new random variable as Z=X+Y. Find P(Z=k).
Let X be a Poisson random variable with parameter λ and Y an independent Bernoulli random...
Let X be a Poisson random variable with parameter λ and Y an independent Bernoulli random variable with parameter p. Find the probability mass function of X + Y .
Let X and Y be independent random variables each having the uniform distribution on [0, 1]....
Let X and Y be independent random variables each having the uniform distribution on [0, 1]. (1)Find the conditional densities of X and Y given that X > Y . (2)Find E(X|X>Y) and E(Y|X>Y) .
a. Suppose X and Y are independent Poisson random variables, each with expected value 2. Define...
a. Suppose X and Y are independent Poisson random variables, each with expected value 2. Define Z=X+Y. Find P(Z?3). b. Consider a Poisson random variable X with parameter ?=5.3, and its probability mass function, pX(x). Where does pX(x) have its peak value?
Problem 0.1 Suppose X and Y are two independent exponential random variables with respective densities given...
Problem 0.1 Suppose X and Y are two independent exponential random variables with respective densities given by(λ,θ>0) f(x) =λe^(−xλ) for x>0 and g(y) =θe^(−yθ) for y>0. (a) Show that Pr(X<Y) =∫f(x){1−G(x)}dx {x=0, infinity] where G(x) is the cdf of Y, evaluated at x [that is,G(x) =P(Y≤x)]. (b) Using the result from part (a), show that P(X<Y) =λ/(θ+λ). (c) You install two light bulbs at the same time, a 60 watt bulb and a 100 watt bulb. The lifetime of the...
Suppose X1 and X2 are independent expon(λ) random variables. Let Y = min(X1, X2) and Z...
Suppose X1 and X2 are independent expon(λ) random variables. Let Y = min(X1, X2) and Z = max(X1, X2). (a) Show that Y ∼ expon(2λ) (b) Find E(Y ) and E(Z). (c) Find the conditional density fZ|Y (z|y). (d) FindP(Z>2Y).
Topic: Linear Combination Of Random Variables Suppose X and Y are independent random variables with X...
Topic: Linear Combination Of Random Variables Suppose X and Y are independent random variables with X ∼ N(1, 9) and Y ∼ N(2, 16). Find the probability that 2Y ≥ 1; find the probability that X − Y ≥ 0.