Question

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.

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

Answer #1

poisson probability distribution |

P(Y=y) = e-λλy/y! |

where y =0,1,2,3 -------------

Binomial probability is given by |

P(X=x) = C(n,x)*px*(1-p)(n-x) |

where X = 0,1,2,3,4,5

since, X and Y are independent, joint probability distribution function will be

so, P(X=x,Y=y) = P(X=x) * P(Y=y)

**P(X=x,Y=y) =Σ5C x * 0.3^ x * (1-0.3)^(5-x) *
e-66y/y! where, x=0,1,2,3,4,5 and y
=0,1,2,3,4...................**

please revert for doubts and

please UPVOTE the solution

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.
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.

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.
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.

Let
X be a binomial random variable with parameters n = 500 and p =
0.12. Use normal approximation to the binomial distribution to
compute the probability P (50 < X ≤ 65).

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 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

Independent random variables X and Y follow binomial
distributions with parameters(n1,θ) and (n2,θ). Let Z =X+Y. What
will be the distribution of Z?
Hint: Use moment generating function.

The random variable X has a Binomial distribution with
parameters n = 9 and p = 0.7
Find these probabilities: (see Excel worksheet)
Round your answers to the nearest hundredth
P(X < 5)
P(X = 5)
P(X > 5)

Let us assume that the number N of children in a given family
follows a Poisson distribution with parameter
. Let us also assume that for each birth, the probability that
the child is a girl is p 2 [0; 1], and that the
probability that the child is a boy is q = 1?p. Let us nally
assume that the genders of the successive births
are independent from one another.
Let X be the discrete random variable corresponding to...

Let B~Binomial(n,p) denote a binomially distributed
random variable with n trials and probability of success
p. Show that B / n is a consistent estimator for
p.

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?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 22 minutes ago

asked 26 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 31 minutes ago

asked 43 minutes ago

asked 43 minutes ago