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In: Statistics and Probability

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and...

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables.

  1. What are the possible values for (X, Y ) pairs.

  2. Derive the joint probability distribution function for X and Y. Make sure to explain your steps.

  3. Using the joint pdf function of X and Y, form the summation /integration (whichever is relevant) that gives the expected value for X4 + Y + 7.

  4. Using the joint pdf function of X and Y, set up the summation /integration (whichever is relevant) that gives the expected value for X, and COMPUTE its value.

Solutions

Expert Solution

The Poisson PMF is

Or

The PMF of X is .

Or,


1)The possible pairs are

Or,

2)The joint PMF is

3)

4) Now, is found using the moment generating function.

orchestra answered 2 years ago
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