Question
In: Statistics and Probability
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).
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...
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...
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.
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...
Suppose that X is a binomial random variable with parameters n=20 and p=0.7. Choose a wrong...
Suppose that X is a binomial random variable with parameters
n=20 and p=0.7.
Choose a wrong statement about the random variable X.
a.
The maximum possible value of X is 20.
b.
The minimum possible value of X is 0.
c.
The variance of X is 4.2.
d.
The expected value of X is 14.
e.
Pr(X = 19)+ Pr(X = 1)= 1
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=
Suppose that x is a binomial random variable with n = 5, p = .66, and...
Suppose that x is a binomial random variable with
n = 5, p = .66, and q = .34.
(b) For each value of x, calculate
p(x). (Round final
answers to 4 decimal places.)
p(0) =
p(1)=
p(2)=
p(3)=
p(4)=
p(5)
(c) Find P(x = 3).
(Round final answer to 4 decimal
places.)
(d) Find P(x ≤ 3).
(Do not round intermediate calculations.
Round final answer to 4 decimal places.)
(e) Find P(x < 3).
(Do not round intermediate calculations....
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Non-constant growth model: Do=$2.00 required return on equity= 5% g= 9% n=1,2 g=7% n=3,4 g=3% n=5...
- . Find all x ∈ Z143 such that x2Ξ 7 (mod 143). Please explain all steps...
- #Python: A palindrome is a sequence of characters that reads the same backwards as forwards. For...
- Explain an example in which a variable has two different addresses at different places in a...
- Hadley, a thirty-five-year-old physician, has worked at Princeton Plainsboro Hospital for six years. She recently received...
- QUESTION 1. For each of the following, state whether the occurrence of the variable x occurs...
- According to Mike Taft of RVK, the “Markets Group” is an important unit of the Federal...
ADVERTISEMENT