Question

The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution.

(a) Identify the graph of the uniform density function.

(b) What is the probability of generating a number between

0.740.74

and

0.910.91?

(c) What is the probability of generating a number greater than

0.930.93?

Answer #1

We are given a random number generator that generates a uniform
random variable X over the interval [0, 1]. Suppose we flip a fair
coin and if H occurs, we report X and if T occurs, we report 2X +
1. Let Y be the reported random variable.
(a) Derive the cdf and pdf of Y
(b) Which one is more likely to occur: Y ∈ [0,1] or Y ∈ [1,2]?
Explain your answer.

The typical computer random number generator yields numbers
from a uniform distribution of values between 0 and 1, with a mean
of 0.500 and a standard deviation of 0.289. If random numbers are
generated, find the probability that their mean is between 0.6 and
0.7.

a continuous random variable X has a uniform distribution for
0<X<40
draw the graph of the probability density function
find p(X=27)
find p(X greater than or equal to 27)

Let X be a random number between 0 and 1 produced by a random
number generator. The random number generator will spread its
output uniformly (evenly) across the entire interval from 0 to 1.
All numbers have an equal probability of being selected. Find the
value of aa that makes the following probability statements
true.
(a) P(x≤a)=0.8
a=
(b) P(x < a) = 0.25
a=
(c) P(x≥a)=0.17
a=
(d) P(x>a)=0.73
a=
(e) P(0.15≤x≤a)=
a=

We are given a random number generator that generates a uniform
random variable X over the interval [0,1]. Suppose we ﬂip a fair
coin and if H occurs, we report X and if T occurs, we report 2X +
1. Let Y be the reported random variable.
(a) Derive the cdf and pdf of Y [15 points].
(b) Which one is more likely to occur: Y ∈ [0,1] or Y ∈ [1,2]?
Explain your answer [10 points].

Random number generator 1:
Search for algorithms generating pseudo-random numbers. Select one
of them for generating a pseudo-random sequence. Original sample
can be generated in any form: binary, decimal, etc. But submitted
sample must be in the form of uniform random numbers on [0,1][0,1].
The sample should not be generated by any function, like runif(),
sample(), etc. Instead it must be some algorithm that you code
yourselves. For example, mid-square algorithm, Fibonacci-based
algorithm, etc.
Random number generator 2:
Find some...

In the following probability distribution, the random variable
x represents the number of activities a parent of a
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through (f) below.
x
0
1
2
3
4
P(x)
0.395
0.075
0.199
0.195
0.136
(a) Verify that this is a discrete probability
distribution.
This is a discrete probability distribution because the sum of
the probabilities is ___and each probability is ___ (Less than or
equal to 1; Greater than or equal...

Lottery Number generator page 335 #2.
Design a program that generates a 7 digit lottery number. The
program should have an Integer array with 7 elements. Write a loop
that steps through the array, randomly generating a number in the
range of 0 through 9. Use the random number generator function.
Then write another loop that displays the contents of the
array.
Create a flowchart using FLOWGORITHM. Please provide
screen shot of flowchart using ONLY FLOWGORITHM and a sample
output.

A random number generator picks a number from two to
ten in a uniform manners
X~__________ (Hint: what X represents?)
Graph the probability distribution.
Find the Mean
Find the Standard deviation
P(3.6 < x < 7.45) =

1. Groups of adults are randomly selected and arranged in groups
of three. The random variable x is the number in the group who say
that they would feel comfortable in a self-driving vehicle.
Determine whether a probability distribution is given. If a
probability distribution is given, find its mean and standard
deviation. If a probability distribution is not given, identify the
requirements that are not satisfied.
x P(x)
0 0.355
1 0.434
2 0.187
3 0.024
a.) Does the...

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