Question
In: Math
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 |
Solutions
milcah answered 9 months agoRelated Solutions
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.)
(a)
P(15 ≤ X ≤ 20)
p
P(15 ≤ X ≤ 20)
P(14.5 ≤ Normal ≤ 20.5)
0.5
0.6
0.8
(B)P(X...
(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 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)
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).
For a binomial probability distribution, n = 130 and p = 0.60. Let x be the...
For a binomial probability distribution, n = 130 and p = 0.60.
Let x be the number of successes in 130 trials. a. Find the mean
and standard deviation of this binomial distribution.
a. Find the mean and the standard deviation of this binomial
distribution.
b. Find to 4 decimal places P(x ≤ 75) using the normal
approximation. P(x ≤ 75) =
c. Find to 4 decimal places P(67 ≤ x ≤ 72) using the normal
approximation. P(67 ≤ x...
Binomial Distribution. Suppose that X has a binomial distribution with n = 50 and p =...
Binomial Distribution. Suppose that X has a binomial
distribution with n = 50 and p = 0.6. Use Minitab to simulate 40
values of X.
MTB > random 40 c1;
SUBC > binomial 50 0.6.
Note: To find P(X < k) for any k > 0, use ‘cdf’ command;
this works by typing:
MTB > cdf;
SUBC > binomial 50 0.6.
(a) What proportion of your values are less than 30? (b) What is
the exact probability that X will...
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