Using excel with formulars
for binomial random variable X with n=10, p=0.3, plot its pdf
and...
Using excel with formulars
for binomial random variable X with n=10, p=0.3, plot its pdf
and cdf; then simulate from it a sample of size N=2000, plot its
histogram (relative frequency), and cumulative frequency.
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 =
Plot using RStudio
Consider a binomial random variable, X.
i. Plot the pmf of X ∼Bin(n = 10, p = 0.3).
ii. Plot the pmf of X ∼Bin(n = 10, p = 0.7).
iii. Plot the pmf of X ∼Bin(n = 100, p = 0.3).
iv. What happens to the shape of the pmf of X ∼Bin(n, p) when p
gets larger?
v. What happens when n gets larger
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 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 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...
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....
Assume that x is a binomial random variable with n = 100 and p =
0.40. Use a normal
approximation (BINOMIAL APPROACH) to find the
following: **please show all work**
c. P(x ≥ 38) d. P(x = 45) e. P(x > 45) f. P(x < 45)
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=
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).