10. , Let X(1 ≤ k ≤ n) be independent random variables and B~ Bernoulli(pk)(1 ≤ k ≤ n) be independent from each other and from the first class of random variables (Σk=1 Pk = 1). Define the mixture random variable X = B₁.X₁ + ··· + B₁-Xn- Calculate the hazard function of X in terms of hazard function of its components. Hint: First, use conditioning to calculate the probability density function and cumulative distribution function of X. Then, use the definition of the hazard function.

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A: We have given, A continuous random variable X has the following CDF: F(x) = 1 - 1x+14, x > 0.

Q: ~x(n) (32) i=1 Exercise 11. Suppose X1, X2,.,Xn is an i.i.d. sample of observations of a random…

A:

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A:

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A: It is given that X1, X2,...., Xn is a random sample from Uniformα-β, α+β.

Q: i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and…

A: It is given that  X follows N(θ, 1), then E(X) = θ and V(X) = 1, And the moment genarating function…

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A:

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A: It is given that  X follows N(θ, 1), then E(X) = θ and V(X) = 1,

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A: Option b) is correct.

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A: Expected value is used for discrete or continuous probability function. It is calculated by the…

Q: Let X(n,p) denote a binomial random variable with parameters n and p. Show that X(n+1,p)>=st X(n,p).

A: Given To prove that

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A: Dear student, If you find this solution helpful please upvote it. The solution is given below :

Q: There are three random variables X, Y and Z,for which we know the following information E(X)= 6,…

A: Given,V(X)=18  ,  V(Y)=22   ,   V(Z)=4Cov(X,Y)=-12   ,  Cov(X,Z)=5Cov(Y,Z)=8

Q: 2. Let X be a random variable with the Poisson distribution, parameter 2. Show that, for w = 1, 2,…

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Q: Suppose §1, $2, ... are iid random variables having mean u and variance o?. Form the random sum SN =…

A: Given that ξ1, ξ2, ..., ξn are iid random variables having mean μ and variance σ2.  SN=ξ1+ξ2+...+ξN

Q: 5. Let X and Y be independent random variables such that X - exp(A) and Y ~ exp(). (a) What is the…

A: It is an important part of statistics. It is widely used.

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A:

Q: (b) Determine e so that п п c£[(x; - X;)² i=l j=1 is an unbiased estimator of o². s2 ogunl to

A: 6. From the given information, X1,.....,Xn~f be an iid random sample with mean μ and variance σ2. a)…

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A: Sol

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

A:

Q: There are three random variables X, Y and Z, for which we know the following information E(X)= 6,…

A: Given: There are three random variables X, Y and Z. The given values are:…

Q: (a) (b) Find E(W). Find Var(W).

A: Given,let  be  independent random variables.E(Yi)=μ and Var(Yi)=σ2  for every since (a)we want to…