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Q: If X, Y and Z are three random variables, then cov (X +Y,Z) =cov(X,Z)+cov(Y,Z)

A: Solution

Q: bet X and Xe be two random variable such that the Condiional distribuhons and means exist. Show thak…

A: Here's the explanation is as follows; Part a) First we need check the identities conditioning on X2…

Q: ii) Let X be a random variable taking three values: P(X= a₁) = P₁, P(X=a₂) = P2, P(X=a3) = P3, where…

A: Given Information: Let X be a random variable taking three values: PX=a1=p1, PX=a2=p2, PX=a3=p3,…

Q: Let X, Y and Z be three independent random variables such that E(X)=E(Y)=2E(Z)2 and…

A: Given information: EX=EY=2EZ=2That is,E(X)=2E(Y)=2E(Z)=1EX2=EY2=EZ2=10 Consider, VX=EX2-EX2…

Q: Let X and Y be random variables with µX = 1, σX = 2, µY = 3, σY = 1, and ρX,Y = 0.5. Find the means…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

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Q: Suppose that V and W are random variables with Cov(V, W) = 0. Which of the following must also be…

A: Solution : V and W are random variable  If V and W are independent  so E(VW) = E(V).E(W) Cov(VW) =…

Q: Suppose we have two random variables X and Y. For a, b > 0, a2+b2=13. Var(aX) = 16 Var(bY) = 36…

A: Suppose we have two random variables X and Y. For a, b > 0, a2+b2=13. Here we use the…

Q: 11 and ơ-2. Find each of the Suppose x is a normally distributed random variable with following a)…

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Q: 7) Let X a random variable with pmf P(X = x|N) =*= 1,2,..N, and let Y = 2X +1, where a, be R then EY…

A: The pmf of X is PX=x|N=1N The expectation of X is given by…

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: Let the random variable Z = k+ mW. Then, Pz = mµw- %3D

A: Given: Z=k+ mW   E(Z)=μZ E(W)=μW

Q: Q1 Suppose X₂ N(μ, o²), i = 1,2,...,n and Z; ~ N(0, 1), i = 1, 2, ..., k, and all random variables…

A: Given independent random variables,  and  are independent.

Q: A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white…

A: We have two random variables X and Y such that  PYy=0     p0=121     p1=12 The conditional density…

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

Q: Suppose that X andY are random variables with E(X) = 2 , E(Y) = 5 and E(X²) = 8, E(Y?) = 30 and…

A: Given that ; E(x) = 2   ;    E(x2 ) = 8  ; E(y) = 5  ;    E(y2 ) = 30 By using these information we…

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: Consider an experiment in which the number of pumps in use at each of two eight-pump gas stations…

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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: The common probability function of the random variables x1 and x2 is as follows (X1x2 X1 = 1,2,3 X2…

A: Y1=X1X2  then, possible values of y1 is as follows: Y1 1 2 3 4 6 9 Situations (Total…

Q: 3. Hand in Use mgf's to prove that if X1, X2, X3, X4 are independent n(0,1) random variables, then U…

A: Here, we have to prove that,        if X1,X2,X3,X4 are independent n(0,1) random variables then…

Q: If X and Y are independent U (–1, 1) random variables then E (min (X,Y))

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Q: We have the following information about the random variables X and Y: |x=2, |y=−1 , ox = 0.25, c X…

A: a)It is given that, .

Q: If Xn, n > 1, independent random variables and Xn 4 X (a random variable X), are

A: A degenerate distribution (sometimes called a constant distribution) is a distribution of a…

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Q: For a discrete random variable X if : Points ) P ( X = x ) = 0.1x , x = 2 , 3 , 5 , then E ( X2 ) =

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Q: The joint PMF of two random variables X and Y is given by (k(2x + y), ((2x) Pxy (x, y) 0, Where k is…

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Q: Consider an experiment in which the number of pumps in use at each of two eight-pump gas stations…

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Q: Assume that a discrete random variable X such that V(X) = 6.5. Find the value of V

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Let X and Y be two random variables. Suppose we know E(X) = 7 and E(Y)=3. Let Z = X − Y be a random…

A: Given EX=7 and EY=3.Let Z=X-Y.Then,E(Z)=4

Q: Where does the z=2 come from? Just from X, and Y also being random variables?

A: Solution of the asked question is in step below.

Q: Page 143, 2.6.6*. Let X₁, X₂, and X3 be three random variables with means, variances, and…

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Q: Suppose we have three independent random variables X, Y and Z where... Var(X + 2Y) = 13, Var(2Y +…

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Q: 4. Show that if X and Y are independent random variables, then E(9(X)| X = ro) = g(ro). %3D

A: We need show that if X and Y are independent random variables, then E(g(X) | X = xo) = g(xo).

Q: If U and V are two independent standard normal random variables and Z=0.6U+0.8V. Determine Corr (U ,…

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Q: Suppose X is a random variable with E(X) = 0 and Var(X) = 2. What is E(X2 )? a). 1 b). 2 c). 3 d).…

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Q: 4. Suppose we have random variables W and Q, and we know Var(W) = 25, Var(Q) = 10, and Cov(W, Q) =…

A: Given,Var(W)=25Var(Q)=10Cov(W,Q)=2

Q: A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white…

A: From the given information, fXx=∑yfX|Yx|ypYy, 0≤x≤100fX|Yx|0=31001-x1002fX|Yx|1=3100x1002PY0=PY1=12…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!