68. Let Xi, . . . , Xn be an 1.1.d. sample from a Poisson distribution with mean λ, and a. Show that the distribution of Xi, , Xn given T is independent of λ, and conclude that T is sufficient for λ. b. Show that X is not sufficient. c. Use Theorem A of Section 8.8.1 to show that T is sufficient. Identify the functions g and h of that theorem.

Q: Suppose that X has the following discrete distribution: x = 1,2,3,4 f(x) = {0.1x, = {*"o, 0,…

A: Given discrete distribution is, fx=0.1x, x=1,2,3,4 x 1 2 3 4 f(x) 0.1 0.2 0.3 0.4 Graph of…

Q: Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2 If σ2 is…

A: Given: Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2 σ2…

Q: An interval within which we expect 95% of all xx's to fall can be defined for any population by…

A: Given that  An interval within which we expect 95% of all xx's to fall

Q: 18. Let the random variables Y, X, X, .. be independent, suppose that YE Fs(p), where 0 < p < 1, and…

A:

Q: Suppose that the conditional distribution of Y given X = x is Poisson with mean A E(Y|x) = x, and…

A: Probability distributions

Q: Prove that in a Poisson distribution (i) Mean m and (ii) S.D. = Vm.

A: Here we have to show that  in a poisson distribution  i) mean=m ii) S.D=m

Q: Suppose X1,..., Xn F with mean µ and variance o². (F is a general (b) distribution and not…

A:

Q: Let O be a Gaussian random vorjable with mean = 4.8 and standord deviation N=2.5. 13D Arondom vari a…

A: Solution: From the given information,

Q: Suppose x has a distribution with u = 12 and o = 7. (a) If a random sample of size n = 45 is drawn,…

A: Central Limit Theorem for mean: If a random sample of size n is taken from a population having mean…

Q: If N = 48, find tcv and use it to draw a t distribution with the rare and common zones labeled.…

A: The t – critical values would be obtained from the t – distribution at certain alpha% level with…

Q: Let X1, X2,..,X, are drawn from a geometric distribution with pmf p(x) = (1-6e)*-', x = 1,2,3,. .…

A:

Q: Suppose X has a Poisson distribution with parameter A and suppose the conditional distribution of Y…

A:

Q: Let X denotes the number of fish captured in a trap during a day. Suppose that X has a Poisson…

A: Given, X ~ Poisson(λ = 3)             To find, P (X ≥ 9 ) = ? in two days.

Q: Let X₁, X₂ be a random sample from N (1,1) and Y₁, Y₂ be a random sample from N (0,1), where the…

A:

Q: If x has Uniform distribution over (1,2) and P(xSc+u) = 0.2 then c is equal to Select one: O a.-0.7…

A: From the given uniform distribution we find the constant C.

Q: (ii) If X is a Poisson distribution such that 2 P(X = 0) + P(X=2) = 2P(X= 1). find E(X). %3D %3D

A: It is given that,  70% of the tiger inoculated with serum are protected from a certain disease i.e.…

Q: Find the minimal sufficient statistics for each of the following cases: (a) Poisson(A) (b)…

A: We know that the minimal sufficient statistic is a function of the sample that provides the greatest…

Q: If the conditional distribution of Y, given X with parameter x and if the unconditional distribution…

A:

Q: Suppose x has a distribution with u = 62 and o = 8. A USE SALT (a) If random samples of size n = 16…

A:

Q: 1. Given n independent and identically distributed observations Y1,., Yn, from an exponen- tial…

A:

Q: Which would be the appropriate command in Excel to calculate the following? What is the probability…

A: The average is 4.

Q: If x is approximately  Poisson, compute ( P(X=2), Px=10, pX=0, pX=0.5. If the mean = 3

A:

Q: Let (X1,X,,X3) be a random sample of size n=3 from Uniform distribution on the interval (0, 0) where…

A: Uniform distribution : Let X  X ~ Ua,b then The PDF is given as; fx = 1b-a     ;  a ≤ x ≤ b0…

Q: 4. Let X= (X1,..., Xn)' be a random sample of size n from a Poisson(A) distribution. Determine if t…

A:

Q: Suppose that components have weights that are normally distributed with u = 100 and o = 10. An…

A: We have given that  We have given that.   X~N( μ , ?^2 )   μ =100 , ? =10 , n= 25    Z-score =( x -…

Q: If ø,(@) is a characteristic function of a random varlable d, function of Y = aX +b is given by P,…

A:

Q: If T, is the RV denoting the time of occurrence of the nth event in a Poisson process with parameter…

A:

Q: Suppose that X has the discrete uniform distribution on the integers 0,1,2 (i.e. P(X = k) = 1/3, k =…

A: P(X=0) = P(X=1) = P(X=2) = 1/3 = 0.333   Y is binomial random variable n = 2 p = 0.5   Y = 0 P(0) =…

Q: ) Suppose that a failure of a certain component follows the distribution f(x) = p²(1-p)'- or x= 0,…

A: Given that p(x)=px(1-p)1-x μ=pσ=p(1-p)

Q: Q.4 (a) Define random Poisson points (RPPs), and prove from first principles that their number in a…

A: Poisson point processes are a type of random mathematical object composed of randomly placed points…

Q: Suppose that X and Y are independent, X~B(10, 0.5), Y follows Poisson distribution with parameter 4.…

A:

Q: Suppose x has a distribution with u = 30 and o = 24. (a) If a random sample of size n = 35 is drawn,…

A: The mean of the sampling distribution of the sample mean. The standard of the sampling distribution…

Q: If X has the Poisson distribution with P(X=1) = 2P(X=2), then P(X ≥ 2) is approximately:

A: Obtain the probability that X greater than equals 2. The probability that X greater than equals 2is…

Q: Let x1 ~ N(0,1), X2 ~N(-1,4) and X3~N(1,9) be independent.  Derive the distribution of Y=x1-x2-2x3…

A: Normal Distribution: A continuous random variable X is said to follow Normal distribution with…

Q: 26 Use Theorem 6.6.5 to establish that, given a sample X1,...,Xn, the following statistics are…

A: Given that -

Q: 1. Let X, 2 Poisson(A,), for i = 1,2. (a) Show that X1 + Xy~ Poisson(A + A2). (b) Show that X| X + Y…

A:

Q: Suppose x has a distribution with u = 19 and o = 14. A USE SALT (a) If a random sample of size n =…

A: Here, μ=19 and σ=14.

Q: Each of 180 newly manufactured items is examined and the number of scratches per item is recorded…

A: Given: n = 180 Number of scratches per item 0 1 2 3 4 5 6 7 Frequency 23 39 39 38 16 9 13 3…

Q: Let X be a random sample of size n from N(41,0}) and let Y be a random sample of size m from N(µ2,…

A:

Q: Now calculate np and nq forn = 20, p = 0.50, and q = 0.50. np = x (0.50) %3D ng = 20 We conclude…

A:

Q: 2. Suppose that x has a distribution with u = 100 and o = 48. %3D 2.a. If a random sample of size…

A: Mean = 100Standard deviation = 48

Q: Let X~N, (u, Σ) 1. size n = 10 with μ' = (5 -2 4) 6 5 -3 Σ= 5 7 0 -3 0 4 find the distribution of X,…

A:

Q: Let X~N, (1,2) μ'=(5-24) 6 5 -3 Σ= 5 7 0 -3 0 4 1. find the distribution of X, and (X₂, X₁) X₁ - X₂…

A:

Q: and Let Let X~ N(μ, E), where -- () Σ: = Y = 11214 121 12 14121 2 (X3+ X₁) 2X2 X3 - X₁ i) What is…

A:

Q: Compute the probability that at least one call will arrive in the next two minutes. 2. Find the…

A:

Q: #4: Suppose that X1,... , X7n is an i.i.d. random sample drawn from a U[a, 1] uniform distribution,…

A:

Q: The central limit theorem says that the sampling distribution of the sample mean is approximately…

A: Solution: It is needed to explain about the central limit theorem.

Q: Let x1, X2, ..., Xn be a random sample from a continuous uniform distribution with domain (0,b).…

A: Here,  Given that,x~U(0,b)fx(x)=1b, 0&lt;x&lt;b0    otherwise

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.