Question
In: Statistics and Probability
Prove that the variance of a random variable with negative binomial distribution (with parameters ? and...
-
Prove that the variance of a random variable with negative binomial distribution (with parameters ? and ?) is ?(1 − ?)/?^2.
-
Prove that the variance of a random variable with hypergeometric
?−? ? ? distribution (with parameters ?, ?, ?) is (M-n)/(N-1) ?(M/N) (1 − (M/N)) .
3. Prove that the variance of a random variable with uniform distribution (with parameters ? and ?) is ((a-b)^2)/12 .
Solutions
orchestra answered 1 year agoRelated Solutions
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...
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).
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 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...
If x is a binomial random variable, compute the mean, the standard deviation, and the variance...
If x is a binomial random variable, compute the mean, the
standard deviation, and the variance for each of the following
cases:
(a) n=3,p=0.9
μ=
σ^2=
σ=
(b) n=6,p=0.1
μ=
σ^2=
σ=
(c) n=4,p=0.6
μ=
σ^2=
σ=
(d) n=5,p=0.8
μ=
σ^2=
σ=
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 binomial random variable with parameters n and p represents the number of successes in n...
A binomial random variable with parameters n and p represents
the number of successes in n independent trials. We can obtain a
binomial random variable by generating n uniform random numbers 1 2
n U ,U ,...,U and letting X be the number of i U that are less than
or equal to p. (a) Write a MATLAB function to implement this
algorithm and name the function gsbinrnd. You may use the for loop
to generate random numbers. (b) Use...
(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.
Use Excel to generate the probability distribution for a binomial random variable for which there are...
Use Excel to generate the probability distribution for a
binomial random variable for which there are 20 trials (n = 20) and
the probability of success is 0.5 (p = 0.5), and show the
graph.
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