Given a Poisson random variable x, where the average number of times an event occurs in...
Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time or space is 1.5, then P(x = 2) is:
| a. |
0.5 |
|
| b. |
0.5020 |
|
| c. |
0.2510 |
|
| d. |
0.2231 |
|
| e. |
0.1116 |
Homework Answers
| A | B | C | D | E | F | G | H | I | J | K |
| 2 | ||||||||||
| 3 | As per Poisson distribution, the probability of observing k events over time is | |||||||||
| 4 | P(X=k) = (λke-λ)/k! | |||||||||
| 5 | ||||||||||
| 6 | Where λ is the average number of times the event occurs over the time period. | |||||||||
| 7 | ||||||||||
| 8 | Since the average number of times an event occurs in a certain period of time is 1.5 | |||||||||
| 9 | therefore | |||||||||
| 10 | λ | 1.5 | ||||||||
| 11 | Thus the probability that the even will occur twice in the given period of time can be calculated as follows: | |||||||||
| 12 | P(X=2) | = (λ2e-λ)/2! | ||||||||
| 13 | 0.2510 | =POISSON.DIST(2,D10,FALSE) | ||||||||
| 14 | ||||||||||
| 15 | Hence the probability is | 0.2510 | ||||||||
| 16 | Thus the option (c) is correct. | |||||||||
| 17 | ||||||||||
Add Answer to:
Given a Poisson random variable x, where the average
number of times an event occurs in...
Poisson Distribution Question Problem 2: Let the random variable X be the number of goals scored...
Poisson Distribution Question
Problem 2: Let the random variable X be the number of goals scored in a soccer game, and assume it follows Poisson distribution with parameter λ 2, t 1, i.e. X-Poisson(λ-2, t Recall that the PMF of the Poisson distribution is P(X -x) - 1) e-dt(at)*x-0,1,2,.. x! a) Determine the probability that no goals are scored in the game b) Determine the probability that at least 3 goals are scored in the game. c) Consider the event...
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
An input source for an electrical system is modeled by a discrete random variable X where...
An input source for an electrical system is modeled by a discrete random variable X where X takes on a value at random from sample space S={1, 2, 3, and 4} volts with corresponding CDF of this random variable, F X ( x ) = {0.2, 0.3, 0.7, and 1.0}. (a) Find P X ( x ), the PMF of this random variable. (b) Let event B be P [ X < 3]. Find P[B]. (c) Find the expected value...
new random variable X is distributed as Poisson) in this question. We create a U where...
new random variable X is distributed as Poisson) in this question. We create a U where its probability mass function is P(X u) u) P(X 1) P(U for u = 1,2,... (a) Show that e P(U u)= 1- e-A u!' for u 1,2,. (6 marks) expression for the moment generating function of U (7 marks (b) Derive an (c) Find the mean and variance of U (7 marks)
new random variable X is distributed as Poisson) in this question. We...
Consider the random sum S= Xj, where the X, are IID Bernoulli random variables with parameter p and N is a Poisson rand...
Consider the random sum S= Xj, where the X, are IID Bernoulli random variables with parameter p and N is a Poisson random variable with parameter 1. N is independent of the X; values. a. Calculate the MGF of S. b. Show S is Poisson with parameter Ap. Here is one interpretation of this result: If the number of people with a certain disease is Poisson with parameter 1 and each person tests positive for the disease with probability p,...
A coin is tossed three times. X is the random variable for the number of heads...
A coin is tossed three times. X is the random variable for the number of heads occurring. a) Construct the probability distribution for the random variable X, the number of head occurring. b) Find P(x=2). c) Find P(x³1). d) Find the mean and the standard deviation of the probability distribution for the random variable X, the number of heads occurring.
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A...
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by C 3Y2. If Y, Y2, Y denote the observed number of breakdowns for n independently selected days, find an MVUE for E(C).
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by...
Problem 1 A Poisson process is a continuous-time discrete-valued random process, X(t), that counts the number of events...
Problem 1 A Poisson process is a continuous-time discrete-valued random process, X(t), that counts the number of events (think of incoming phone calls, customers entering a bank, car accidents, etc.) that occur up to and including time t where the occurrence times of these events satisfy the following three conditions Events only occur after time 0, i.e., X(t)0 for t0 If N (1, 2], where 0< t t2, denotes the number of events that occur in the time interval (t1,...
The number of messages sent to a computer website is a Poisson random variable with a...
The number of messages sent to a computer website is a Poisson random variable with a mean of 5 messages per hour. a. What is the probability that 5 messages are received in 1 hours? b. What is the probability that fewer than 2 messages are received in 0.5 hour? c. Let Y be the random variable defined as the time between messages arriving to the computer bulletin board. What is the distribution of Y? What is the mean of...
Please answer from a-d Problem 2. Let X be a random variable with one of the...
Please answer from a-d
Problem 2. Let X be a random variable with one of the following cumulative distribution function. 1.2 1,2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2,0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 X X Pick the correct cumulative distribution function plot and answer questions: Page 2 of 9 Write down the probability mass function and What is the PMF of X? A. Poisson (3...
Poisson Distribution Question
Problem 2: Let the random variable X be the number of goals scored in a soccer game, and assume it follows Poisson distribution with parameter λ 2, t 1, i.e. X-Poisson(λ-2, t Recall that the PMF of the Poisson distribution is P(X -x) - 1) e-dt(at)*x-0,1,2,.. x! a) Determine the probability that no goals are scored in the game b) Determine the probability that at least 3 goals are scored in the game. c) Consider the event...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
new random variable X is distributed as Poisson) in this question. We create a U where its probability mass function is P(X u) u) P(X 1) P(U for u = 1,2,... (a) Show that e P(U u)= 1- e-A u!' for u 1,2,. (6 marks) expression for the moment generating function of U (7 marks (b) Derive an (c) Find the mean and variance of U (7 marks)
new random variable X is distributed as Poisson) in this question. We...
Consider the random sum S= Xj, where the X, are IID Bernoulli random variables with parameter p and N is a Poisson random variable with parameter 1. N is independent of the X; values. a. Calculate the MGF of S. b. Show S is Poisson with parameter Ap. Here is one interpretation of this result: If the number of people with a certain disease is Poisson with parameter 1 and each person tests positive for the disease with probability p,...
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by C 3Y2. If Y, Y2, Y denote the observed number of breakdowns for n independently selected days, find an MVUE for E(C).
The number of breakdowns Y per day for a certain machine is a Poisson random variable with mean A. The daily cost of repairing these breakdowns is given by...
Problem 1 A Poisson process is a continuous-time discrete-valued random process, X(t), that counts the number of events (think of incoming phone calls, customers entering a bank, car accidents, etc.) that occur up to and including time t where the occurrence times of these events satisfy the following three conditions Events only occur after time 0, i.e., X(t)0 for t0 If N (1, 2], where 0< t t2, denotes the number of events that occur in the time interval (t1,...
Please answer from a-d
Problem 2. Let X be a random variable with one of the following cumulative distribution function. 1.2 1,2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2,0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 X X Pick the correct cumulative distribution function plot and answer questions: Page 2 of 9 Write down the probability mass function and What is the PMF of X? A. Poisson (3...
Most questions answered within 3 hours.
-
A rifle with a mass of 78 kg fires a bullet with a mass of 36...
asked 35 seconds ago -
Question 10
Applied Materials depreciates buildings and improvements over
useful lives of 5-50 years.
a.
True....
asked 20 minutes ago -
A 10.0 mL sample of 0.25 M NaOH(aq) is titrated with 40.0 mL of
0.10 M...
asked 21 minutes ago -
How
can we prove that a flow is incompressible if the velocity field is
known?
asked 23 minutes ago -
It is sometimes argued that understanding people's existing
activities does not really help to design future...
asked 27 minutes ago -
what is the angular velocity of tje moon in its orbut ( orbit
period is 28)?
asked 28 minutes ago -
Time Off At Superior Software Service
As she hangs up the telephone, Joan Jackson realizes that...
asked 31 minutes ago -
Use the sample data and confidence level given below to complete
parts (a) through (d).
A...
asked 33 minutes ago -
1. Consider a risky portfolio. The end-of-year cash flow derived
from the portfolio will be either...
asked 34 minutes ago -
Find the critical value(s) for the specified Wilcoxon
signed-rank test.
Sample size = 10, two-tailed test,...
asked 1 hour ago -
why don't arctic animals feet freeze in winter biology
question
asked 51 minutes ago -
Cellular respiration in eukaryotes has the same purpose as
fermentation in prokaryotes
True
False
asked 52 minutes ago