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Probability Questions
Probability Questions
Question 1
Let 𝑋 be a standard normal random variable
Let 𝑋 be a standard normal random variable.
Heads and Tails
Consider a sinusoidal signal with random phase, defined by x(t)=Acos(2πfct+θ), where A and FC are constant and θ is a random variable uniform distributed over interval [-π,π], that is f(θ)={█(1/2π,&-π≤θ≤π@0,&elsewhere)┤ Describe the autocorrelation RX(τ
Question (1) Find the value of the constant k, so that f(x) = kx3,0 < x < 1 is a probability density function of random variable X and then calculate: i. The distribution function F(X), and draw it. ii. The mean E(X) and the variance V(X) of the random va
There are N sites that need protection (number them 1 to N). Someone is going to pick one of them to attack, and you must pick one to protect. Suppose that the attacker is going to attack site i with probability qi. You plan on selecting a site to protect
When doing polling, for instance to figure out how popular a given candidate is, a common trick is to just ask N many people whether they support that candidate, and take the support to be the faction of people who say yes: if 70 people support the candid
Exercise - 2.15
Statistics
Probability Question
Given the following distribution function F(x) = { 1 - e^-0.05x , x≥0 a) find the probability density function of X b) find P(5 ≤ x ≤ 10).
Write the definition of E[Y | X = x].
Statistics Question
Find the joint density function of coloured balls sampling
Use 68-95-99.7 rule
The owners of a competitor company to Uber has its own application called "Pridej" and they attempt to optimise the starting time of their mobile application. Calculate the probability that the download of the maps is longer process than loading of drive
For one roll of a dice, let A be the event "even" and let B be the event "2 or 4." Find P(B|A)
Hypothesis test
A container contains 30 tokens
Suppose that 4 cards are drawn from a well-shuffled deck of 52 cards.
Find correlation coefficient
Show me the whole solution thank you so much :)
I need help with this question
probability
Statistics
Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean, based on the following sample size of n=8.
The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $8.20. Assume the stock prices are normally distributed. What is the probability a company will have a stock price between $20 and $40? How high does a stoc
Conditional Probabilities
Use a Venn Diagram. Let P(Z)=0.47, P(Y)=0.24, and P(Z ∪ Y)=0.56. Find each probability. (a) P(Z′ ∩ Y′) (b) P(Z′ ∪ Y′) (c) P(Z′ ∪ Y') (d) P(Z ∩ Y') Complete the Venn diagram below using the given probabilities. I can't figure out how to find th
The random variable X has density function F(x)= (k+1)x^2 for 0
The random variable X has density function F(x)= (k+1)x^2 for 0
Find the mass function of Y.
math 115 statistics
NUMBER 3, please.
Random process- Probability
The points problem
Six individuals, including A and B, take seats around a circular table in a completely random fashion. Suppose the seats are numbered 1, …, 6. Let X= A's seat number and Y= B's seat number. If A sends a written message around the table to B in the directi
Suppose your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time. a. If you take the bus each morning and evening for a week,
Ex. 52 The lifetime of a certain type of battery is normally distributed with mean value 10 hours and standard deviation 1 hour. There are four batteries in a package. What lifetime value is such that the total lifetime of all batteries in a package excee
Ex. 46. The inside diameter of a randomly selected piston ring is a random variable with mean value 12 cm and standard deviation .04 cm. a. If ?̅ is the sample mean diameter for a random sample of n= 16 rings, where is the sampling distribution of ?̅ cent
Ex. 36 Show that if Y= aX+ b (a≠0), then Corr(X, Y) = +1 or -1. Under what conditions will p = +1?
Ex. 24 Six individuals, including A and B, take seats around a circular table in a completely random fashion. Suppose the seats are numbered 1, …, 6. Let X= A's seat number and Y= B's seat number. If A sends a written message around the table to B in the
Ex. 10 Annie and Alvie have agreed to meet between 5:00 P.M. and 6:00 P.M. for dinner at a local health-food restaurant. Let X = Annie's arrival time and Y= Alvie's arrival time. Suppose X and Yare independent with each uniformly distributed on the interv
A stockroom currently has 30 components of a certain type, of which 8 were provided by supplier 1, 10 by supplier 2, and 12 by supplier 3. Six of these are to be randomly selected for a particular assembly. Let X= the number of supplier 1's components sel
70. If X has an exponential distribution with parameter ⋋, derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median.
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation .1 cm. The second machine produces corks with diameters that h
Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. a. P(0 ≤ Z ≤ 2.17) h. P(1.37 ≤ Z ≤ 2.50) i. P(1.50 ≤ Z) j. P(|Z| ≤ 2.50)
Math 1140
What is the probability of II-2 AND II-3 having two children that have the same autosomal recessive disease as their siblings?
Suppose that in a day, the probability of insurance agents not closing any deal is 0.3. On the other hand, the probability the he can close deal is 0.25; two deal 0.35 and three deals, 0.1. Find the agents expected number and variance of close deal in a d
Suppose a workstation receives parts automatically from a conveyor. An accumulation line has been...
Find PDF, Mean and Variance and ?(|?| < 1.5)
Mean and Variance of Probability mass function
binomial distribution
gamma density functions
quiz consists of 8 multiple choice questions. each question has 5 answers, one of which is correct. if random guess is made, find the probability that 1 answer will be correct
Suppose that the n random variables X1, ..., Xn form a random sample from the discrete distribution with f(k) = ( 2 −(k+1) for k = 0, 1, 2, . . . ; 0 otherwise. Find P(X1 = X2 = ... = Xn).
Let X be a random variable, which has a binomial distribution with parameters n and p. It is known that E(X) = 12 and Var(X) = 4. Find n and p.
A researcher wishes to estimate, with 99% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. His estimate must be accurate within 5% of the population proportion. (a) No preliminary estima
An unreliable company produces a large shipment of blenders where 15% have a defective motor, and 23% have a defective electrical cord and 11% have both defects.
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = (p^x) [(1 − p)^(1−x)]
In the general population, IQ is normally distributed with a mean 100 and standard deviation 15.....
Assume that 12 jurors are randomly selected from a population in which 72% of the people are Mexican-Americans.
Develope CTMC
CTMC
Statistic
What is the probability of a randomly selected will order both a chicken sandwich and french fries
Conditional distribution given joint density of (X,Y)
Suppose that the average number of airline crashes in a country is 2.5 per month.
Let f(x)={cx^9y^4 if 0≤x≤1, 0≤y≤1 0 otherwise Find the following:
Suppose that the average number of airline crashes in a country is 2.5 per month.
According to the U.S. National Center for Health Statistics, 25.2 percent of men and 23.6 percent of women never eat breakfast. Suppose that random samples of 175 men and 175 women are taken. Approximate the probability that
Suppose that for two random variables X and Y the joint density function is f(x,y)=2xe^−x(y+2), for x>0 and y>0. Find each of the following.
Probability
Probability
Probability
Probability
Probability
The two continuous random variables, X1 and X2, are independent and have the same pdf, ?4x3 : 0≤x≤1, fX1 (x) = fX2 (x) = 0 : otherwise. Define the two variables U and V as follows. U = X ?X , V = X ?X . 21 1. Find the joint pdf of U and V. 2. Find and plo
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