Let X1, X2, .. ,Xn form a random sample from B(1,0). Find minimal sufficient statistics.

Q: Suppose that Y, Y2.,Yn parameter (2,8+ 4). are independent random variables from a gamma…

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Q: how to find E(X), E(Y), E(X^2)

A: Given that X and Y are independent and follows N(0,1)

Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

Q: A box contains 5 Balls labeled with the number "1", 3 balls labeled with the number "2", and 1 ball…

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Q: A data processing company has a training program for new salespeople. After completing the training…

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Q: Suppose the variance of the difference of two random variables X and Y is zero. Then, show that X =…

A: A random variable is a function that associates a real number with each element in the sample space.…

Q: Two independent random variables X and Y have 36 and 16.Find the correlation co-efficient between…

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Q: Suppose that f (x) = e* for 0 < x Determine the mean and variance of the random variable.

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Q: Let X1 and X2 be two independent normal random variables with parameters (0,1) and (0,4)…

A: X1 and X2 are two independent normal variates  mean and variance (0,1) and (0,4) respectively. Then,…

Q: Let Y₁, Y2, ..., Yn be a random sample from a population with a Gamma distribution with parameters a…

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Q: Let X1, X2, ..., Xn ~ exp(A) be a random sample. Show that X is sufficient for 1/A.

A: Given:  X1,x2,.....xn from exponential distribution with parameters lambda  Then to show that xbar…

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

A: Given that X1 follows Normal distribution with E(X1)=2 and V(X1)=3. X2 follows normal distribution…

Q: If X1, X2, ...Xn is a random sample from N(0, σ^2), How would you show the following?

A: The critical region C defined as C={(x1​,x2​,...,xn​):∑i=1n​xi2​≥c} is the best critical region for…

Q: Let x be a dis crete random variable with probability distribution fCx) =k (x² + 20) and x =…

A: i. From the given information, the probability distribution function is f(x) = K (X2 + 20) and x=…

Q: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

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Q: Find the joint probability function of (X,Y) where

A: Provided information is, two cards are drawn at random from a box which has 5 cards numbered 1, 2,…

Q: 4- Let X₁, X₂,..., Xn be a random sample fromBeta(0, 1) and 0~1(a, p). Find the bayes estimate of 0.

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Q: Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the…

A: The correlation coefficient between two random variables X and Y is defined as:  ρ(X, Y) = Cov(X, Y)…

Q: Assume that the population consists of only these eleven data points for y and z. Construct one…

A: It was stated to assume that the population consists of only these eleven data points for y and…

Q: Let a and b be any real numbers and let x = (x,. Xz ----Lp --,L) be a data set with a sample mean f…

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Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

A: Given Data: Var(X)=8 Var(Y)=6

Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

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Q: dataset x = (x1, … , xn ) has sample variance of 0 when (n≥2 ). prove that all the data points are…

A: This problem is based on the sample variance and data sets.   To show -  If sample variance is zero…

Q: A data processing company has a training program for new salespeople. After completing the training…

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Q: Let Y1, Y2, Y3, Y4, and Y, be i.i.d. random variables from a population with mean u and variance o?.…

A: given data let y1,y2,y3,y4 and y5 be random variablesand givenW=18y1+18y2+15y3+15y4+720y5

Q: X is a discrete random variable such that the possible values are {a, a+1, a+2, ... b-1, b}. The…

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Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

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Q: Let xy X2 ..., Xn be a random sample from a Poisson distribution with parameter A. Find ML estimator…

A: ANSWER:  For the given data,

Q: The probability distribution of the discrete random variable X is 3-x x = 0,1,2,3. .4, Find the…

A: Solution-: We have the p.m.f. of X is given by,  f(x)=3x*(14)x*(34)3-x f  ;  x=0,1,2,3;   We find…

Q: An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t)…

A: In this case, the random variable R defines the number of tails.

Q: Assume a population with 5 elements: X1-0, X2-1, X3-2. X4-3.x5-4 Calculate mean and variance of X…

A: Given information: The population is of size 5. It is required to draw samples of size 3 with…