Question

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 X^4 + 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.

----------------------------

DEAR STUDENT,

IF YOU HAVE ANY QUERY ASK ME IN THE COMMENT BOX,I AM HERE TO HELPS YOU.PLEASE GIVE ME POSITIVE RATINGS

*****************THANK YOU**************

orchestra answered 3 years ago
Next > < Previous

Related Solutions

Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3
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. (a) What are the possible values for (X, Y ) pairs. (b) Derive the joint probability distribution function for X and Y. Make sure to explain your steps. (c) Using the joint pdf function of X and Y, form...
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. What are the possible values for (X, Y ) pairs. Derive the joint probability distribution function for X and Y. Make sure to explain your steps. Using the joint pdf function of X and Y, form the summation /integration...
Let X be a binomial random variable with parameters n = 5 and p = 0.6....
Let X be a binomial random variable with parameters n = 5 and p = 0.6. a) What is P(X ≥ 1)? b) What is the mean of X? c) What is the standard deviation of X? (Show work)
(a) Let X be a binomial random variable with parameters (n, p). Let Y be a...
(a) Let X be a binomial random variable with parameters (n, p). Let Y be a binomial random variable with parameters (m, p). What is the pdf of the random variable Z=X+Y? (b) Let X and Y be indpenednet random variables. Let Z=X+Y. What is the moment generating function for Z in terms of those for X and Y? Confirm your answer to the previous problem (a) via moment generating functions.
Let X be a binomial random variable with n = 11 and p = 0.3. Find...
Let X be a binomial random variable with n = 11 and p = 0.3. Find the following values. (Round your answers to three decimal places.) (a)     P(X = 5) (b)     P(X ≥ 5) (c)     P(X > 5) (d)     P(X ≤ 5) (e)     μ = np μ = (f)    σ = npq σ =
The p.d.f of the binomial distribution random variable X with parameters n and p is f(x)...
The p.d.f of the binomial distribution random variable X with parameters n and p is f(x) = n x p x (1 − p) n−x x = 0, 1, 2, ..., n 0 Otherwise Show that a) Pn x=0 f(x) = 1 [10 Marks] b) the MGF of X is given by [(1 − p) + pet ] n . Hence or otherwise show that E[X]=np and var(X)=np(1-p).
A random variable Y whose distribution is binomial with parameters are n = 500 and p=...
A random variable Y whose distribution is binomial with parameters are n = 500 and p= 0.400, and here Y suggests the number of desired outcomes of the random experiment and n-Y is the number of undesired outcomes obtained from a random experiment of n independent trials. On this random experiment   p̂ sample proportion is found as Y/n. (Round your answers to 3 decimal places in all parts.) a)What is the expected value of this statistic? b)Between what limits will...
Let x be a random variable that possesses a binomial distribution with p=0.5 and n=9. Using...
Let x be a random variable that possesses a binomial distribution with p=0.5 and n=9. Using the binomial formula or tables, calculate the following probabilities. Also calculate the mean and standard deviation of the distribution. Round solutions to four decimal places, if necessary. P(x≥3)= P(x≤8)= P(x=5)= μ= σ=
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = 0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x; n, p). (Round your answers to four decimal places.) (a) P(15 ≤ X ≤ 20) p P(15 ≤ X ≤ 20) P(14.5 ≤ Normal ≤ 20.5) 0.5 1 2 0.6...
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of...
Let X have a binomial distribution with parameters n = 25 and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases p = 0.5, 0.6, and 0.8 and compare to the exact binomial probabilities calculated directly from the formula for b(x; n, p). (Round your answers to four decimal places.) P(20 ≤ X) p P(20 ≤ X) P(19.5 ≤ Normal) 0.5 0.6 0.8
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT