If X is an exponential random variable with parameter 1, and c > 0, show cX is expor

Q: Ifp and q are independent variates uniformly distributed over the interval (-1, 1), find the…

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Q: The profit for a new product is given by Z= 3X- Y- 5. If X and Y are independent random variables…

A: Answer - Given, Z = 3X - Y - 5             X and Y are independent random variables  with σx = 1…

Q: Suppose X is a discrete random variable with finite first and second moments. Show that E (x…

A: It is given that X is a discrete random variable with finite first and second moment.

Q: Derive u and show that 7 X is biased estimator of 2. Can you modify 7T -X in order to get an…

A: The expected value of X is defined as  μ=∫λ∞x.f(x)dx And an estimator to be unbiased its expected…

Q: Let X₁, X₂, Xa be a random sample taken from uniform gepulation U (0-1,0 + 1). Show that the median…

A: Given information: The random samples X1, X2, and X3 follows Uθ-12,θ-12.

Q: 2. Suppose that X is a random variable with E(X) = 6 and Var(X) = 4. Find the following: a) Е(4X +…

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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: 5. If X is an exponential random variable with parameter 2, and c > 0, show cX is exponential with…

A: Using transformation of cumulative distribution

Q: . Let a random variable X - U(5,5+0). Based on a single observation X1, find the unbiased estimator…

A: # random variable x follow uniform (5,5+theta) then to find unbiased estimator of theta^2

Q: E(Y) –> P(Y > n).

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Q: (2x-x*), 2x-x²), 0<xs2 Suppose X is random variable whose p.d.f. is f(x)={4 0, elsewhere Find the…

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

Q: Express the variance of the variable X in terms of n.

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Q: Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with…

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Q: If X is a random variable, prove that Cov(X,X) = σX².

A: Let X is a random variable.

Q: Jim’s bookcase holds 4 geometry books, 1 calculus book, and 3 algebra books.  Books are taken at…

A: Total number of books in the bookcase is 8  (4 +3+1)   Number of books other day algebra book  is 5…

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: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

Q: Suppose that the joint CDF of the random variables X and Y is given by 0, x < -2 or y < –5

A: Given that Fx,y=0, x&lt;-2 or y&lt;-538, -2≥x&lt;2, -5≤y&lt;312, x≥2 and -5≤y&lt;312, -2≤x&lt;2 and…

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: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.2, an

A: Given information: Var(X)=1.6 Var(Y)=1.2 Cov(X,Y)=0.6 Let  Z = -1.2X + 1.9Y + 4.2.

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: The cdf of a random variable Y is |1– exp(-0.4y), y 20 F,(y) otherwise Valuate P{2.5 <Y < 6.2}.

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Q: obtain the MVB estimator for u in normal population. №.(402), where 2 is know

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Q: If the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 -…

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Q: Assume I observe 3 data points x1, x2, and x3 drawn independently from the same unknown probability.…

A: From given data we have : Prx1|M=0.5,Prx2|M=0.1,Prx3|M=0.2.

Q: Let X be a random variable such that a. V(3x-3) b. E(3x-3) E(X²) = 58 and V(X) = 40. Compute

A: Answer:- Given, X be a random variable such that  E(X2) = 58 and V(X) = 40               (a) Find…

Q: Is cov(X, Y) random?

A: Given :Is cov(X, Y) random?

Q: Show that for two random variables X and Y, 2 2 var(aX+bY) = a¹o²+b²oy² + 2ab Cxx XY where a and b…

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Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor    Therefore,  X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

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: Suppose that X is a geometric random variable with parameter π. Show that P(X = n+k|X > n) = P(X =…

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Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.5, and Cov(X, Y) = 0.1. Let Z =…

A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

Q: Let X1, …, Xn be independent lognormal random variables and let a1, …, an be constants. Show that…

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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: If X is a random variable with expectation µ and variance cµ2 , where c is a constant. Find a…

A: X= random variable expectation µ and variance cμ2 where c is constant then we need to find the…

Q: Suppose that the joint CDF of the random variables X and Y is given by: 0, x < -2 or y < -5

A: Given that Consider, the density function,

Q: Suppose that P(A)=0_25 and P(B) =x and P(AUB)= 0.7 For what choice of x are A and B independent? non…

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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

Q: if x1, X2, ., X, be a random sample from Bin(4,0). ........ is T = x UMVUE ? Justify your answer.

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Q: Show that if X, Y are independent random variables, then Cov(X, Y ) = 0.

A: Given that X and Y are independent random variables.