Q2 Suppose Y is a discrete random variable such that P(Y= y) = K(1-a)-1,0 < a <1 for y = 1,2,... co. Find the following as an expression of a. a) Value of the unknown K b) The mean and variance of Y.

Q: 3. Let X1, X2, ..., X, be a random sample from a normal population with mean u and variance a2 taken…

A: Please see the attachment......

Q: Let X1, X2, X3 be i.i.d. random variables N(0, 1). Show that Y1 = X1+8X3 and Y2 = X2+8X3 have…

A: Solution:         ut   x1    x2 , x3    iid ~N(u=0, α2=1)         ut  Y1 = x1 +δ x3 &amp; y2= x2+δx3…

Q: B2. Let A₁,..., An> 0 and let X₁,..., Xn be independent random variables with common mean E(X) = μ…

A: This question deals with the minimum variance of the estimator μ^(X1,X2,...,Xn) for the mean μ given…

Q: The random variable X is distributed normally with mean µx and variance 6, and the random variable Y…

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Q: 1. Random variable X has p.d.f 6e-6z I>0 fx(x) = %3D otherwise and let Y = eX. (b) (i.e. Calculate…

A: Probability density function gives the probability at each possible value of random variable X. The…

Q: 3. Let Y₁,...,Y be a random sample of size 5 from a normal population with mean 0 and v n 15 ΣY. Let…

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Q: If Y₁ = ettet-1+e-2 3 ', PY₁,Y₁-2 find E(Y), var(Y), cov (Yt, Yt-1), cov (Yt, Yt-2), PY,Y, and…

A: Given that,and is an iid (independent and identically distributed) random variable with zero mean…

Q: ru+1.50/VR 1-1.20/VE()*dr.

A: As per bartleby guideline if more than one question asked, only first question to be answered.…

Q: Q1. interest y Consider the following bivariate data of an independent variable x and dependent…

A: The given data is x y 0 3 0 2 1 1 1 0 2 0 3 -1 4 -2 6 -15

Q: m-1 j=) t is the distribution of Y,? State all the relevant parameters of the evel a test (that is,…

A: Write the distribution of Yi bar and state its all the relevant parametersWrite the distribution of…

Q: Let w₁, W2, ..., wt be independent random variables from a normal distribution with mean 0 and…

A: Let w1, w2, ..., wt be independent random variables from a normal distribution with mean 0 and…

Q: 3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probability…

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Q: A) Caused by a third variable B) uncorrelated ) negative effect 0.fb/ orrrte D) direct…

A: The correlation coefficient formula is given by

Q: (a) Show that X² is not an unbiased estimator for the area of the square plot p². [Hint: for any rv…

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Q: b. Suppose of = 2, o% = 2.5, and m = n. Find the sample size n so that X - Ý will be within one unit…

A: X1,X2,...,Xm and Y1,Y2,...,Yn are two samples with  Xi~ N(µ1 ,σ1)  , Yi~ N(µ2 , σ2)  All the random…

Q: An optical device is used to detect the passage of cars in a single lane of a downtown street.…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: 4. Suppose the joint PDF of two random variables X and Y are given below. |3(ry? + x²y), if 0 < x <…

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Q: Suppose you have a joint distribution of x and y where • x has population mean lg and population…

A: Disclaimer: " As per guideline we can answer only one question can be solved. So, If you want to get…

Q: Question 2. Let X be a normal random variable with u = -5 and o² = 4. a) Find P(X –3|X > -5).

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Q: Suppose that X is a random variable for which the m.g.f. is as follows: M(t) = 1/4(3et+e-t), -∞<t<∞…

A: We can get the mean and variance after finding the first and second derivative of mgf at t= 0