Question
In: Statistics and Probability
If X is a random variable with the given distribution, determine – without calculations! – which...
If X is a random variable with the given distribution, determine – without calculations! – which of the two probabilities is higher or if they have to be equal. Explain your answer.
(a) P{−1 6 X 6 4} and P{10 6 X 6 15}, where X ∼ Uniform(−10, 20).
(b) P{−1 6 X 6 4} and P{10 6 X 6 15}, where X ∼ Normal(2, 3).
Solutions
orchestra answered 2 years agoRelated Solutions
Given a random variable X that has a t(ν) distribution, determine the value of xo such...
Given a random variable X that has a t(ν) distribution,
determine the
value of xo such that P (|X | <xo)=0.025
for (i) ν = 5; (ii) (i) ν = 25; (iii)
ν = 50; (iv) ν = 100. Compare your results with the single value of
x0 such that
P (|X | <x 0)=0.025 for a standard normal random variable 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...
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
7. Suppose that we are given that there exists a random variable X whose distribution is...
7. Suppose that we are given that there exists a random variable
X whose distribution is binomial with parameters are n = 500 and p=
0.300, and here X represents the number of desired outcomes of the
random experiment and n-X is the number of undesired outcomes
obtained from a random experiment of n independent trials. From
this random experiment p̂ sample proportion is found as
X/n. (Round your answers to 3 decimal places in all
parts.)
What is the...
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
Given a random variable X following normal distribution with mean of -3 and standard deviation of...
Given a random variable X following normal distribution with
mean of -3 and standard deviation of 4. Then random variable
Y=0.4X+5 is also normal.
(1)Find the distribution of Y, i.e. μy,σy
(2)Find the probabilities P(−4<X<0),P(−1<Y<0)
(3)Find the probabilities P(−4<X¯<0),P(3<Y¯<4)
(4)Find the 53th percentile of the distribution of X
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. If so, give...
Determine whether or not the random variable X is a binomial
random variable. If so, give the values of n and p. If not, explain
why not.
a. X is the number of dots on the top face of fair die that is
rolled.
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...
Show that the cumulative distribution function for a random variable X with a geometric distribution is...
Show that the cumulative distribution function for a random
variable X with a geometric distribution is
F(x) = 0 for x < 0,
F(x) = p for 0 <= x < 1,
and, in general, F(x)= 1 - (1-p)^n for n-1 <= x < n for n
= 2,3,....
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