Question

Consider the following question and determine if the *random
variable* X is **C**ontinuous or
**D**iscrete. Select a *distribution* to use
from the options to find the exact probability in question. Select
either **U**niform, **B**inomial,
**P**oisson, **N**ormal, or
**E**xponential. Do not solve the problem simply
explain how you arrived at your conclusion when selecting the
random variable and the selected distribution.

Question:

You have taken a sample from a batch of parts and have averaged the diameter of the parts in the sample. You want to know the probability that the sample average is less than 1.25 inches.

Answer #1

**X---- Will be
Continuous Random Variable .**

**Explanation:**

**Continuous Random Variable:** A
**variable** is a quantity whose value changes between
any point or interval. This is real quantity. **Here,
Diameter is a continuous Number.**

A **discrete random variable** is a variable whose
value is obtained by counting.

**And
Distribution Will be Normal Distribution**

**Explanation:**

**In Normal Distribution we take sample distribution of
sample mean. And then find their Probability .**

**In Normal Distribution , distribution is symmetric about
sample mean.**

What kind of variable has values determined by chance?
random variable
discrete variable
continuous variable
Question 5
A binomial distribution is a probability distribution for a:
discrete random variable
continuous random variable
Question 6
A normal distribution is a probability distribution for a:
continuous random variable
discrete random variable
Question 7
Which is not a property of the binomial distribution?
only two outcomes
fixed number of trials
constant probability of success
dependent outcomes

Calculate the probability that X ≤ E[X] assuming that: (a) X is
a continuous random variable with uniform distribution; (b) X is a
continuous random variable with an Exp(1) distribution; (c) X is a
discrete random variable with a Poisson(1) distribution. (d) X is
continuous random variable with standard normal distribution.

Determine whether the following value is a continuous random
variable, discrete random variable, or not a random variable.
a. The number of textbook authors now eating a meal.
b. The "yes" or "no" response to a survey question"yes" or "no"
response to a survey question
c. The time required to upload a file to the Internet time
required to upload a file to the Internet
d. The number of free dash throw attempts before the first shot
is missed a...

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...

Determine whether the random variable is discrete or continuous.
A. The number of people in a restaurant that has a capacity of 100.
B. The weight of a feather C. The exact life span of a kitten. D.
The number of supermodels who ate pizza yesterday.

A continuous random
variable X denote the time between detection of a particle with a
Geiger counter. The probability that we detect a particle within 30
seconds of starting the counter is 0.50.
The random variable X
has the "Lack of memory" property that After waiting for three
minutes without a detection, the probability of a detection in the
next 30 seconds is the same as the probability of a detection in
the 30 seconds immediately after starting the counter....

Determine whether the random variable is discrete or continuous.
In each case, state the possible values of the random variable.
(a) The number of people with blood type Upper A in a random
sample of 50 people. (b) The time required to download a file from
the Internet.

1. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate E(X)
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
2. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate the variance of X
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
3. Given a discrete random variable, X...

Let X be a binomial random variable with n =
400 trials and probability of success p = 0.01. Then the
probability distribution of X can be approximated by
Select one:
a. a Hypergeometric distribution with N =
8000, n = 400, M = 4.
b. a Poisson distribution with mean 4.
c. an exponential distribution with mean 4.
d. another binomial distribution with n =
800, p = 0.02
e.
a normal distribution with men 40 and variance 3.96.

If X is a discrete random variable with uniform distribution,
where f(x) > 0 when x = -1, 0, and 1(f(x) = 0, otherwise). If Y
is another discrete random variable with identical distribution as
X. In addition, X and Y are independent.
1. Please find the probability distribution of (X + Y)/2 and
plot it.
2. Please find variance of (X + Y)/2

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