If x and y are independent random variables then f(y\x) equal f(x) f(xy) f(y) non of them

Q: Let X and Y be two independent N(0,1) random variables and consider Z = 3+ X + YX , Ww = 3 + Y. Then…

A: Result  If X and Y are independent then  E(g(X)h(Y))=E(g(X))E(h(Y)) Cov(X,Y)=0

Q: If fx₁x₂ (x₁, x₂) is a joint density function, then find the joint density function of Y, and Y₂

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

A: Solution: From the given information,

Q: Let u(X) be a nonnegative function of a random variable X. It can be shown that  P(u(X) >= c) = a)…

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

Q: If xy Xy .... Xy is a random sample from the distribution. f (x, 0) er (1- 0)-x, x = 0, 1 and 0< 0<1…

A: Answer: For the given data,

Q: Prove that P (a SX< b) = Fx (b) -Fx (a)

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Q: Let X and Y be two random variables and let r, s, t, and u be real numbers. a. Show that Cov(X+s,…

A: Given: X and Y be two random variables and let r, s, t, and u be real numbers.  We have to show that…

Q: Let X and Y be random variables with finite variance. Prove that |ρ(X, Y)| = 1 implies that there…

A: Let's assume that |ρ(X, Y)| = 1, which means that the correlation coefficient between X and Y is…

Q: Find fQ|X (q|x) for x ∈ {0, 1} and all q.

A: It is a fact of statistics. It is widely used.

Q: E(Y) –> P(Y > n).

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Q: The mean and variance of a random variable X which is uniformly distributed on the interval (a, b)…

A: The mean of the function can be calculated from the density function. If f(x) is the density…

Q: There are only two states of the world, when a person is well with probability (1-p) and i with…

A: From the given information, A person is well with probability 1-p A person is ill with probability…

Q: c) Suppose that X and Y are jointly continuous random variable - x f(x,y) = {o* for 0< x <1 and 1< y…

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Q: Let X and Y be two independent N(0,1) random variables and consider Z = 3 +X+ 2XY² , W = 5 + X. Then…

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Q: The CDF F(x) of a random variable X is given by; F(x) = { 0, if x 3 } i) the mean and variance of…

A: Here,fx=dfxdx=dcx-14dx=4cx-13                                    ;1&lt;x≤3   Now, find c using the…

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

A: Solution

Q: Suppose that X, and X2 are aiscrete random variables with joint pdf of the form f(x1,x2) = c(x1 +…

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Q: Given that random variable X is continuous type, we form the random variable Y as Y = g (x) = 6 F,…

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Q: Assume Y=1​+X+u​, where X​, Y​, and ​u=v+X are random​ variables, v is independent of X​; E(v​)=0,…

A: According to the provided data, Y=1+X+u where X, Y, and u=v+X are the random variables. It is…

Q: Let X be a non-negative random variable that is not a constant. The product E(1/X) times E(X) is…

A: The question is asking whether the product of the expected value of a non-negative random variable X…

Q: ). If X is a continuous random variable whose pdf is f(x): (a) 0 (b) 1 (c) 1/4 (d) 4 (e) None of the…

A: 0 \)" data-mce-style="cursor: default;"&gt;f(x)=c(1+x)4;x&gt;0

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi.…

A: Understanding the Pressure Relationship in TiresKnowing the air pressure in one tire of a vehicle…

Q: (4) If a point x is taken at random on the interval [0, 2a] and all the points are equally likely to…

A: Given :x2a-x&gt;a22

Q: (4) If a point x is taken at random on the interval [0, 2a] and all the points are equally likely to…

A: the selection of a point in the closed interval [0,2a] is a uniform random variable X.

Q: Let X be a random variable. Find E(Y) where 3 Y = (X – E(X)) (a) 1 (d) Q (b) 3/4 (e) -1 (с) —3/4 -

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Q: Suppose the random variable y is a function of several independent random variables, say…

A: Given that the random variable y is a function of several independent random variables, say…

Q: Find the covariance between x and y

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Q: If X and Y are two independent random variables, then E(XY) = E(X) E(Y)

A: We need to prove, E(XY)=E(X).E(Y) It is given that X and Y are independent random variables,

Q: If X and Y have the joint probability distributionf(−1, 0) = 0, f(−1, 1) = 1 4 , f(0, 0) = 16 , f(0,…

A: The joint probability distribution of the random variables is given as follows:

Q: Let P(x) denote the probability of the occurrence of event x. Plot all those points (x, y) = (P(A),…

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Q: random process of x(t) is defined by x(t)=Acos(at) + Bsin(at), where A and B are two andom variables…

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Q: what is E[XY]?

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Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: Given,f(x)=k(x-x4)     ; 0≤X≤10                 ; other wise

Q: Let V=X+Y and U=X-Y are random variables, then the condition which make the covariance

A: Given that V=X+Y and U=X-Y are random variables. Formula for covariance between U and V is…

Q: Q1 Let X be a non-negative discrete random variable. Prove that the expected value of X satisfies…

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Q: Show that (a) Cov(aX, bY)= ab Cov(X,Y). (b) Cov(X+a, Y + b) = Cov(X,Y). (c) Cov(X, aX+b) = a Var(X).

A: Let (X ,Y) be a bivariate random variable and a, b be real constants. Covariance measures joint…

Q: 8. IFX is a continuous random variable and y = ax + b then the expected valued of y = ? a. aE(x) b.…

A: y=ax+b

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

A: # Given CDF of random variable x  F(x)=1-2^-x     : x&gt;0  let y=max(x1,X2,x3)   To find…

Q: Let X1, X2, X3 be random variables each having a mean u and variance o'. Further, Cov(X1 X2) 2,…

A: The mean of a constant is equal to the value of the constant and the mean of sum of random variables…

Q: Property 3. If X is a random variable and ´a' is constant, then E [a ¥ (X)] = a E [Y (X)] E [Y (X) +…

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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!