Show that if E,=1 a, diverges, then En=1 | |a,| diverges. %3D

Q: 2. Construct the CDF of X if the pdf is given by f(x) = (1 − ²) (2,6)(x).

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Q: dæ x-1 1

A: Solution: The objective is to find whether the given integral converges or not

Q: erence in receiving the signals from both stat ath where the ship experiences the same tir

A: Difference in distance between the ship and the two stations is given by:  ∆d=c∆t Where ∆t is time…

Q: A) S diverges B) S converges none of these

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Q: 1. Let X1,..., X, be independent, X; ~ exp(A;). a. Show that Y min(X1,..., Xn) is also exponential…

A: The exponential distribution is a continuous type distribution. The density function is defined as…

Q: 1 E(-1)"+1, ( n + 1 ) . 3η n=1

A: To find whether converges or diverges

Q: A random variable X has a pdf 1 cosx ーπ fx (x) ={2 2 2 elsewhere Find the mean value of the function…

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Q: The causal sequence {x} Xg = (G)* (k> 0) %3D XK Determine the z transform

A: given                                                xk=12k; (k≥0) we have to find z-transformation.…

Q: A continuous random variable X has a pdf of the form: f(x) = (562/803) x^3, for 1.66 <X<1.91.…

A: The density function of random variable X is: f(x) = (562/803) x3          for  1.66 &lt; x &lt;…

Q: F of X and be-byu(y)

A: It is given that X and Y are independent events andZ=X+Y. The value of fXx is , fXx=ae-axux. The…

Q: Question 2 (a) Let X; be the number of errors on the i-th page of code. Suppose that the X;'s are…

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Q: + cx, –1<x<0 , 0<x<3 0, otherwise 15 64 f (x)={-

A: Calculate the value of constant “c” by using the sum property of distribution. So, the density…

Q: k log k Show that diverges. 1+ k2 k=1

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Q: Let X have the pdf f(x) = B¬l exp{-x/ß}, 0< x<o∞o. Find the moment generating function, the mean,…

A: The moment generating function is defined as MX(t) = E(etx)

Q: a) Find the moment generating function of X. b) Use the MGF to find E(X) and Var(X).

A: Let , pdf of a continuous random variable is ,  = 0 ; otherwise Our aim is to find the following :…

Q: ог Question A.) Does this CONVERGE • DIVERGE ? (~) ² M nal

A: To determine whether the given series converges or diverges.∑n=1∞ln n2n

Q: ke the model y = y x'1β1+x'2β2+ϵ with E(xe)=0 Suppose B1 is estimated by regressing Y on X1 only.…

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Q: Question 6. Suppose that Y has the pdf fy(u) = 1, 0 < <1, zero elsewhere. Let X =-7 In(Y). Then, the…

A: The cumulative distribution function is defined as F(x) = P(X ≤ x)

Q: Which test to use and is it convergent/divergent? 1 Σ Z 16n2 – 8n – 3 n=1

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Q: 12. Which of the following best models the population that is continuously growing at 5% per year…

A: population increasing also depends on what is actual population right now     Let f(t) is the…

Q: A random variable X has pdf f(x) =- 1 x= 1,2,3,..,n 2* Find the moment generating function M(v ).

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Q: Bi(n, p) and using the MGF compute Derive the moment generating function of X E[X] and Var[X].

A: Given,A random variable X~Bi(n,p)P(X=x)=nxpxqn-x    ;   X=0,1,2,.....nand q=1-p

Q: 0 1 2 P = 1 When Xo = 0. What is the expected time that the chain visits state 1 for the third time?…

A: In the expected time of the state 1 for the given trancient matrix P. so we will find expected first…

Q: Section 3.7 p. 343/345 # 364 Determine whether the improper integrals converge or diverge. If…

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Q: Example Suppose that Y Poisson(X) and consider testing Ho: A = A ild against H₁ A Av. solve it now

A: Given: Y~Poiλ

Q: 3. If the pdf is -a<x<a ,Find the generating function( express your answer in 2a simplified form)

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Q: PAPER 1 4. INDICES AND SURDS page 39 J2019 1 Given that find the value of each of the constants a, b…

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

Q: 1. Let X1,..., Xn be independent, X; ~ exp(A¡). a. Show that Y = min(X1,..., Xn) is also exponential…

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Q: var 3X+2)-432 a) Find a and 9 If the random variable X has Gamma (@) .such that E(X-2)-10 and 5)…

A: We are given the following information as follows   X ~ Gamma (α,θ) and E(X-2)=10; and Var(3X+2)=432…

Q: If X ∼ Gamma(2, 5), find E(X^2 ) andE(X^4 )

A: Solution: Let X follows gamma distribution with the parameters 2 and 5.

Q: 20) The figure below gives the US consumption of petroleum over a 10 year period. Estimate the…

A: The given chart is  To find: the average consumption .

Q: If a, > 0 and -0 an is convergente then E(an)"2 is also convergente Select one: O True O False

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Q: (a) State and proof circular time shifting property of DFT.

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Q1. [Normal to Lognormal Transformation] Show that if a random variable X ~ Normal(µ, o), then…

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Q: 3. If the pdf is -a<x<a , Find the generating function( express your answer in simplified form)

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Q: Suppose the survival function of the curtate lifetime of a newborn baby is given by 100 – x s(x) = =…

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Q: An estimator 0 for a parameter 0 theta is unbiased if: Elô] = 0 O ô is normally distributed with…

A: Unbiased Estimator: We have an unbiased estimator of a parametr is an estimator whose expected value…

Q: Exercise 1: 1. Let X: Poisson(@), show that whether the p.d.f of X is a member of exponential class…

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Q: ax Examine the convergence of , where a>1. x (log xy" +1

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Q: 0.3 and 0.4 respectively. Le variance of T is? 05

A: Given that  V(A)=0.3 V(B)=0.4 T=5A-2B

Q: Statel O None of these O Regression between X and Y determines the natur variables. Regression…

A: Q

Q: s or diverges. If t

A: we have to tell whether the given series converges or diverges.∑n=2∞1n2-1

Q: Q1 (a) Let X1,...,Xn be iid observations from an exponential(X) pdf, where A has th conjugate IG(a,…

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Q: 7. Suppose that the random variable X have the pdf f(x) = e-/2, x > 0 and 0 otherwise. (a) Find E(X)…

A: Given,

Q: Find P(2 0

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Q: п? + 12 6) E Зп? + 4n — 1 n=1

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Q: er diverge weDedecmineif thefallawing serier converge 20 Ln n 2- 4E4

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Q: Find the mean and standard deviation of S = , X %3D =D1 Confirm that S Poisson(13) Compute P(S = 0).

A: Given that X1 ~ Poisson(2), X2 ~ Poisson(5), X3 ~ Poisson(4), and X4 ~ Poisson(2)

Q: A. Proof that the following Gamma function is: [(n+1)= n[(n)

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: SELEC A) converges B) diverges C) D)

A: The given series is: ∑n=2∞1n3-n