Question

Suppose you wanted to generate a sample of random variable
following binomial distribution with N=5 and p=0.2, but you only
have access to random number generator following continuous uniform
distribution between 0 and 1. How would you do this? (Provide two
solutions)

Answer #1

Develop an algorithm for generation a random sample of size
N from a binomial random variable X with the
parameter n, p.
[Hint: X can
be represented as the number of successes in n independent
Bernoulli trials. Each success having probability p, and
X =
Si=1nXi
, where Pr(Xi = 1) = p, and
Pr(Xi = 0) = 1 – p.]
(a) Generate a sample of size
32 from X ~ Binomial (n = 7, p = 0.2)
(b) Compute...

True or False?
19. In a binomial distribution the random variable X is
discrete.
20. The standard deviation and mean are the same for the
standard normal distribution.
21. In a statistical study, the random variable X = 1, if the
house is colonial and X = 0 if the house is not colonial, then it
can be stated that the random variable is continuous. 22. For a
continuous distribution, P(X ≤ 10) is the same as P(X<10).
23. For...

Suppose X is binomial random variable with n = 18 and p = 0.5.
Since np ≥ 5 and n(1−p) ≥ 5, please use binomial distribution to
find the exact probabilities and their normal approximations. In
case you don’t remember the formula, for a binomial random variable
X ∼ Binomial(n, p), P(X = x) = n! x!(n−x)!p x (1 − p) n−x . (a) P(X
= 14). (b) P(X ≥ 1).

Suppose Y is a random variable that follows a binomial
distribution with n = 25 and π = 0.4. (a) Compute the exact
binomial probability P(8 < Y < 14) and the normal
approximation to this probability without using a continuity
correction. Comment on the accuracy of this approximation. (b)
Apply a continuity correction to the approximation in part (a).
Comment on whether this seemed to improve the approximation.

Suppose that a random variable X has a binomial distribution
with n=2, p=0.5. Find the mean and variance of Y =
X2

Given a random sample size n=1600 from a binomial probability
distribution with P=0.40 do the following... with probability of
0.20 Find the number of successes is less than how many? Please
show your work

Suppose we have a binomial distribution with n trials
and probability of success p. The random variable
r is the number of successes in the n trials, and
the random variable representing the proportion of successes is
p̂ = r/n.
(a) n = 44; p = 0.53; Compute P(0.30
≤ p̂ ≤ 0.45). (Round your answer to four decimal
places.)
(b) n = 36; p = 0.29; Compute the probability
that p̂ will exceed 0.35. (Round your answer to four...

1) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 6, and p = 0.11.
Write the probability distribution. Round to six decimal places,
if necessary.
x
P(x)
0
1
2
3
4
5
6
Find the mean.
μ =
Find the variance.
σ2 =
Find the standard deviation. Round to four decimal places, if
necessary.
σ =
2) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 10, and p =...

Assume that x is a binomial random variable with n and p as
specified below. For which cases would it be appropriate to use
normal distribution to approximate binomial distribution? a. n=50,
p=0.01 b. n=200, p=0.8 c. n=10, p=0.4

suppose a random sample of n measurements is selected from a
binomial population with probability of success p=0.31. given
n=300.
describe the shape, and find the mean and the standard deviation of
the sampling distribution of the sample proportion

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