If X1 and X2 are independent random variables hav-ing binomial distributions with the respective parameters n1 and θ and n2 and θ, show that Y = X1 + X2 has thebinomial distribution with the parameters n1 + n2 and θ.

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A: Suppose that X , Y and Z are statistically independent random variables ~ X2(2) distribution . U = X…

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A: Calculate the moment generating function:

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A: If two random variable X and Y are uncorrelated then Cov(X,Y)= 0 I.e  X and Y are independent. If X…

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A:

Q: Let Y1, Y2, Y3 be independent binomial random variables with probability of success, p=0.4, and…

A: From the given information, Y1,Y2,Y3 be independent binomial random variables with probability of…

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let X be a binomial random variable with parametern=3, p-0.2 then find P(X -0) 0.513 O 0.512 O 0.411…

A: The binomial formula is: This is the case of binomial, as there are only two possible outcomes…

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A: Given Xi~N(μ,1), i=1,2

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Q: Let X1, X2, ... be a sample from a population that is geometrically distributed with p = }. (a) Use…

A: Given: Xi ~ Geometric with p=1/4 Therefore,  E[X] = μ = 1/p = 4   &  Var(X) = σ2 =1/p2 -1/p = 16…

Q: Suppose two independent random variables X1~ uniform[0,2a] and X2 - uniform[0, 2b]. Moreover, an…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Suppose you have two random variables X,Y ux,Hy,o o3,0xY where Cov(X, Y) = 0x.Y You sample both…

A: The provided information is: n=81x¯=50y¯=55σ2x=25σ2y=144σxy=34.50

Q: 1. Show that if X' , Y' are the deviations of the random variables X and Y from their respective…

A: Given that, Xi' and Yi'are the deviations of random variables X and Y form their means. Xi' = Xi-X¯…

Q: If X1 and X2 are independent random variables hav-ing the geometric distribution with the parameter…

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Q: if Y1 and Y2 are independent Poisson random variable with parameters λ1 and λ2 re- spectively. Then…

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Q: rete random variable that possesses a binomial distribution. Using the binomial formula, find P(X=8)…

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Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

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Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

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Q: If X1 and X2 are independent random variables with distribution given by P[Xi] = −1 = P[Xi = 1] =…

A: Construct the PMF of X1X2, So, P(X1X2 = x) = P(X1=1, X2 = 1) +P(X1=-1, X2 = -1)    if x =1P(X1=-1,…

Q: Suppose X1, X2, X3 and X4 are independent random variables, which have the same Bernoulli…

A: Given that  X1, X2, X3, X4 ~ Bernoulli ( p = 1/3 ) X1, X2, X3, X4 are independent  Compute Cov(X1 +…

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Q: Suppose X has the geometric pmf fx(x) = ()*, z = probability distribution of Y = X/(X+1). Note that…

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Q: If the random Variable x has a uniform distribution the interval [0,5] on Find P(2<XS4).

A:

Q: Suppose that X and Y are both binomial random variables with parameters n and p. If Var(X − Y) = 2,…

A: SOLUTION: Cov(X,Y)=np(1-p)-1

Q: Find the distribution of Z X+Y, if X and Y are jointly continuous random variables F given by

A: Given information: The joint probability density function of the random variables X and Y is given.

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Q: Suppose two discrete random variables X and Y follows a Binomial distribution. If the random…

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Q: Suppose that X1, X2, X3 are independent and identically distributed random variables with…

A: # Given CDF kf random variable x  F(x)=1-4^-x  and y =max(x1,X2,x3)  where x1,X2,x3 are iid random…

Q: If X is a discrete random variable with the distribution function p(x) = 3-*; x = 1,2,3 ... Prove…

A: Given that the distribution function of the discrete random variable X as px=3-x  ; x=1, 2, 3 ...…

Q: Let X and Y be two independent random variables distributed uniformly on the interval [0, 1]. What…

A:

Q: If the joint probability distribution of X and Y isgiven byf(x, y) = 130 (x + y) for x = 0, 1, 2, 3;…

A: Given, the joint probability density function:

Q: If X(n,p) is a binomial random variable with parameters n and p, then why is it that X(n+1,p)…

A: Given that X(n, p) is a binomial random variable with parameters n and p.We will prove the given…

Q: If X is a continuous random variable with distribution, f(x) =+k if0sxs3 0 elsewhere Determine P(1…

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Q: If the discrete random variable X takes on the values 1 , 2 , 3 and if P ( X = 1 ) = P ( X = 3 ) =…

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Q: If is a random variable that has a uniform distribution on the interval [0, 10], then p(x+ 27) PX+…

A: Let X be a random variable having a uniform distribution on the interval [0,10], then the pdf of X…

Q: IfX is a random variable that has a uniform distribution on the interval [o, 10], then pfx+ 10 27 is…

A: Let X be a random variable which has a uniform distribution on the interval [0,10], then the pdf of…

Q: An alternative proof of Theorem 2 may be based on the fact that if X1, X2, ..., and Xn are…

A: The pdf of Bernoulli distribution is given by: where x=0 or 1.

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Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=0.5, P(2)=0.2 and…

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Q: Suppose that the probability distribution function for the random variable X is given by: 2X f(X) =…

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Q: Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0. |

A: Given that  X and Y are same distribution thenE(X2)=E(Y2) , E(X)=E(Y) Show that Cov(X+Y,X-Y)=0

Q: Letx X2,bp å dzntically distributed random variables with finite second moment Show that nP [Ix) 7…

A: The answer is given using the concept of normal distribution.

Q: X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are…

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Q: Suppose a random variable Y uniformly distributed over the interval [2, 7]. 1. What is f(y)?

A: It is given that Y follows Uniform(a = 2, b = 7) To find : The probability density function of Y.

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.