Let X, X2, .., X, be a random sample from Poisson population, show that is 71 consistent estimator of A.

Q: Suppose that the number of potholes per randomly se;ected 300 ft stretch of roadway has a Poisson…

A:

Q: Let x be the observed mean of a random sample of size n from a distributionhaving mean μ and known…

A: Confidence interval on μ is given by  x¯-za2σn≤μ≤ x¯+za2σn                  ...........(1)

Q: If Y Poisson(2) and Z Poisson(3) are independent, what is distribution of W = Y + Z?

A: Solution: Given  Y~Poisson(2)    and  Z~Poisson(3)   Y and Z are independent random variable

Q: An estimator for parameter v is consistent if E(v) is close to v when sample size is increased.…

A: Given If E(v) is close to parameter v, the estimator is consistent.

Q: Suppose that X1 and X2 are random variables with zero mean and unit ariance. If the correlation…

A:

Q: The number of road construction projects that take place at any one time in a certain city follows a…

A: X= no. Of project taking place in city Mean = 3 poisson distributaion

Q: Draw all possible samples of size 4 with replacement from a population 1,3,5. Construct a sampling…

A: Given information: Population 1, 3, 5 Sample size = 4 Determine the population mean and standard…

Q: Show that a beta distribution with α=β=1 is the same as the U (0,1) distribution.

A:

Q: From past experience, it was found out that in a certain factory, there is an average of two…

A: Let ,X=no.of accidents per monthX~poisson (λ=2)P(X=x)=e-λ λxx! ; x≥0

Q: Define a continuous random variable.

A: Continuous random variable is given.

Q: Explain the Covariance functions as applicable to random processes.

A: The autocovariance function CX(s,t) of a random process {X(t)} is a function of two times s and t.…

Q: Suppose a radioactive source is metered for 3 hours, during which time the total number of alpha…

A: The probability exactly four particles will be counted in the next 2 minutes by defining X to be the…

Q: Assume that the frequency where a person acquires a fever in a month is given by a Poisson random…

A: Required information: Suppose X be a possion random variable that denotes the frequency where a…

Q: The number of corner kicks in a 90 minute soccer game follows a Poisson distribution with a mean of…

A: Poisson distribution is a discrete function which is used to measure the probability of an event…

Q: Draw all possible samples each of size 2 from the population 12, 6, 24, 30, 18 using sampling with…

A: Given Population size= 12, 6, 24, 30, 18  sample size=2

Q: Let be a geomerric random variable with prf y=1,2,3... where 9 Find. estimator using matimum…

A:

Q: Suppose data X1, ..., Xn are sampled from the population, sample mean is a random variable

A: It is given that Sample : x1, x2,......,xn

Q: The number of road construction projects that take place at any one time in a certain city follows a…

A: Given : mean = λ = 7 Poisson distribution  = e-λ λxx!

Q: Which random variable X is a discrete variable?

A: The number of degrees of the liquid can be in decimal. It can take any real value. So it is a…

Q: a person threw 10 dice 500 times and obtained 2560 times 4,5or 6.can this be attributed to…

A: For 10 dice 500 times roll we have total 500*10=5000 dices drawn, out of which 4,5, and 6 have 50…

Q: If the random variable X follows a Poisson distribution with parameter 7, what is the probability…

A: given ,  X follows poission distribution (λ=7)

Q: Suppose we are interested in the relationship between an individual’s brown hair and ski color.…

A: From the given information, X: degree of brown hair color Y: degree of skin color

Q: A call center agent receives an average of 28 calls per hour. Assuming that this follows a Poisson…

A: Givenaverage of 28 calls per hourλ=28x~poisson(λ=28)P(X=x)=e-λ×λxx! ; x≥0 In poisson distribution…

Q: Let Xi. X2 --- Xn be a random sample from the Poisson _ 8*e¯® distribution . with pmf fix;o)=. Find…

A:

Q: Let X be an exponential random variable with mean 1 and X, a gamma random variable with mean 2 and…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: If the annual proportion of new restaurants that fail in a given city may be looked upon as a random…

A: Given data : ∝=1 , β=4

Q: A researcher claims that a post-lunch nap decreases the amount of time it takes males to sprint 20…

A:

Q: Suppose that the probability of success is p in a Bernoulli trial with success x. Show that the…

A: Bernoulli Trail: In probability theory, a Bernoulli trial is a random experiment which has exactly…

Q: Assume that hybridization experiments are conducted with peas having the property that for​…

A: It is provided that hybridization experiments are conducted with peas having the property that for…

Q: It is known that if bacteria are grown on a maintenance board of area A, and if Y = the number of…

A: We want to find following probability  X~Poisson(μ=5.5)

Q: The number of corner kicks in a 90 minute soccer game follows a Poisson distribution with a mean of…

A:

Q: Suppose that the variable under consideration is normally distributed on each of two populations and…

A:

Q: Suppose that the number of calls coming per minute into an airline reservation center follows a…

A: The random variable X denotes the count of number of calls received per minute. The probability that…

Q: Suppose people immigrate into a territory at a Poisson rate of 2 per day. Assume that 40% of…

A: Given: X ~ Poisson(2*40%)  => X ~ Poisson(0.8)

Q: Prove that for any discrete distribution standard deviation is not less than mean deviation from…

A:

Q: Suppose X1,...,X, is a random sample from an exponential distribution with mean 0. If X = = 17.9…

A: Given Information: X1, X2......Xn is a random sample that follows exponential distribution with mean…

Q: If x and y are independent Poisson variable, show that the conditional distribution of x given x + y…

A:

Q: The average number of collisions in a week during the summer months at a particular intersection is…

A: Given: The average number of collisions in a week during the summer months at a particular…

Q: If a population forms a normal shaped distribution with µ =40 and σ = 8 and a sample of 16 scores…

A: Given: X~Nμ,σμ=40σ=80n=16x¯=36

Q: Suppose that the random variables X₁,..., X and Y₁,...,Y, are random sample from independent normal…

A: It is given that Xi~N(3,8), i=1, 2, … , 8, where 3 is the mean and 8 is the standard deviation. The…

Q: The number of customers arriving per hour at a certain automobile service facility is assumed to…

A: a) Let us define the random variable X as the number of customers arriving per hour follows Poisson…

Q: An average of 3.1 daisies grows in 1 square meter of grass, following a Poisson distribution. Using…

A: Given : An average of 3.1 daisies grows in 1 square meter of grass, following a Poisson distribution…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.