Question
In: Statistics and Probability
Assume the random variable X has a binomial distribution with the given probability of obtaining a...
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X=6), n=10 , p=0.5
Solutions
Expert Solution
P(X = 6) = 10C6 * 0.56 * (1 - 0.5)10-6 = 0.2051 (ans)
orchestra answered 2 years agoRelated Solutions
Assume the random variable X has a binomial distribution with the given probability of obtaining a...
Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X≤4), n=7, p=0.6
Assume the random variable X has a binomial distribution with the given probability of obtaining a...
Assume the random variable X has a binomial distribution with
the given probability of obtaining a success. Find the following
probability, given the number of trials and the probability of
obtaining a success. Round your answer to four decimal places.
P(X=14), n=15, p=0.7
If x is a binomial random variable, use the binomial probability table to find the probabilities...
If x is a binomial random variable, use the binomial
probability table to find the probabilities below.
a. P(x<6) for n = 15, p=0.2
b. P(x>=14) for n=20, p=0.8
c. P(x=23) for n=25, p=0.1
If x is a binomial random variable, use the binomial probability table to find the probabilities...
If x is a binomial random variable, use the binomial
probability table to find the probabilities below.
a. P(x=3) for n=10, p=0.5
b. P(x≤4) for n=15, p=0.3
c. P(x>1) for n=5, p=0.2
d. P(x<6) for n=15, p=0.8
e. P(x≥14) for n=25, p=0.8
f. P(x=3) for n=20, p=0.1
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.
Question 1: Given the following probability distribution for a random variable X: x P(X=x) -2 0.30...
Question 1:
Given the following probability distribution for a random variable
X: x P(X=x)
-2
0.30
-1
0.15
0
0.20
1
0.20
2
0.15
a) Explain two reasons why the above distribution is a valid
probability distribution.
b) Calculate μX and σX.
c) Determine the cdf(X), and write it as an additional column in
the table.
d) Calculate P(−1<X≤3) .
e) Draw a histogram that represents the probability distribution of
X.
Determine whether or not the random variable X is a binomial random variable. (a) X is...
Determine whether or not the random variable X is a binomial
random
variable.
(a)
X is the number of dots on the top face of a fair die
(b)
X is the number of hearts in a five card hand drawn (without
replacement) from a well
shuffled ordinary deck.
(c)
X is the number of defective parts in a sample of ten randomly
selected parts coming from a manufacturing process in which 0.02%
of all parts are defective.
(d)
X...
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).
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
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