1. A continuous r.v X is uniformly distributed on (0.12) and X₁, X₂, X6o are i.i.d r.v.'s with the same distribution as X. For the sample mean X of X₁, X₂, X60 (1) find E(X) and Var (X). (2) approximate P(X> 6.3). ***

Q: Let X1,.X, be a random sample from a uniform (0,0) distribution and let Y = max(X1,..., the coverage…

A: We have a sample X1, X2,....,Xn from uniform distribution.  We know that, Y = max(X1, X2,....,Xn) =…

Q: 7. Let (r1, 12, ., T„) be a random sample from a normal distribution with mean u and a variance o?.…

A:

Q: 4- Suppose that y is N3(4, 41) and let -2 -4 -1 3 -2 -3 A = 4. %3D %3D 1 y Ay, What is the…

A: Given that y~N3μ, 4𝕀 μ=123 and A=2-2-4-1341-2-3

Q: If the variance of a poisson variate is 3. Find the probability that X = 0 i) i) ii) 0<x<3 18x<4

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Q: 27. If X is uniformly distributed over (0, 1) and Y is exponentially distributed 1, find the…

A: X is uniformly distributed over (0, 1) and Y is exponentially distributed with parameter .

Q: 5. Let Y1 01, - 0 0. 02 02 (a) Find the joint pdf of Z1 = Y1, Z2 = Y2 and Z3 = Y1 + Y2 + Y3. (b)…

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Q: For the continuous distribution dF = yo (x -x) dx, 0SxS1. Find the arithmetic mean, the mode and…

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Q: Set n > 2. Let X1, X2, ..., Xn denote a random sample from a uniform distribution on (0, 1) i.e.…

A: Given that,  Xi ~U(0, 1) i= 1,2,3......n We have to find E(R) where R=Y(n) - Y(1)

Q: 1 The continuous random variable X has p.d.f. f(x) where f(x) = ¿x for 0<x<4 = 0 otherwise.

A:

Q: 3. If X is x² (23), find the following: a) P(14.85 < X < 32.01) b) constants a and b such that P(a <…

A: i.e. X follows chi-squared distribution with 23 degrees of freedom.

Q: X is a normally distributed variable with mean μ = 35 and standard deviation σ = 5. Find a) P(x 21)…

A: given that information x is a normally distributed variable with mean μ = 35 and standard deviation…

Q: 6. Given a continuous uniform distribution, show that A+B (a) μ = and 2 (b) 02: (B-A)² = 12

A: The objective of this question is to derive the formulas for the mean (μ) and variance (σ²) of a…

Q: Suppose X1, . . . , Xn are i.i.d. from a continuous distribution with p.d.f. fθ(x)=1/2(1+θx)if…

A: X1, . . . , Xn are independent and identically distributed (i.i.d) random variables with pdf…

Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?

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Q: 2. A random variable X follows Beta(2,3) distribution. (a) Show that the cumulative distribution…

A: Here, Beta(2,3) F(x) = 6x^2 - 8x^3 + 3x^4

Q: X is a normally distributed variable with mean μ = 35 and standard deviation σ = 5. Find a) P(x 21)…

A: Given problem Given that   X is a normally distributed variable with mean μ = 35 and standard…

Q: 3. Let X be a random variable with distribution function P(X ≤x} = { 0 x 1 if x ≤ 0, if 0 1. Let F…

A:

Q: 20. A continuous random variable X has CDF given by if x <1 F(x) ={2(x – 2 + 1/x) if 1<x<2 if 2 < x…

A: As Prof. A. K. Giri defined, "Probability Density Function: A continuous function f(x) is said to be…

Q: Let X N(0, 1), and let Z ~ Unif{-1, 1} (i.e. P(Z = −1) = P(Z = 1) = 1/2) be independent of X. Let…

A: It is given that X~N0,1 and Z=-1       p=0.51          p=0.5 X and Z are independent.

Q: Q5. A continuous r.v. X is said to have a Gamma (a, B) distribution if its moment generating…

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Q: Suppose that Y1,..., Yn is a sample of size n from a Exp(B), B > 0. .3B (a) Find the distribution of…

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Q: 3. If X has a uniform distribution in (0,1) with p.d.f f(x)=1, 0<x<1 = 0, otherwise. Find the…

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Q: 7. Suppose a random sample X₁,..., Xn comes from a continuous distribution f(x|B) = Q(B)g(x)…

A: The continuous distribution of X f(x, β)=Q(β)g(x)I(0&lt;x&lt;β).   To calculate the sufficient…

Q: Let X~ N(0, 1) and let Y = -X. (a) Show that Y~ N(0, 1) (by showing that Y has cdf Þ). (b) What is…

A: X follows a standard normal distribution.

Q: 4. If X~ N3 (μ, E) where µ¹ = [2-3 1] and Σ = 1 3 2 | 1 2 2 then find the distribution of 3X1-2X2 +…

A:

Q: 8. If Z has the distribution N(0,1) and Y has distribution X: 3Z (a) what is the distribution of U =…

A: Given  Z~ N(0,1) and Y~ chisquare with 9 degree of freedom  Find  (a) distribution of U  (b) mean…

Q: If F at the degree of freedom (2, 12), LaTeX: \alpha\:=0.01α = 0.01 and then the number of groups I…

A: The degree of freedom for F ratio is (k-1, N-k), where k is the number of treatment conditions and…

Q: Marginal Distributions For the discrete case: so that for all x₁ E Dx₁. F=Σ Fx (x1) = Σ PX1X2(W1W2)…

A: Here pX1,X2x1,x2 denotes the joint probability mass function (PMF) at X1=x1 and X2=x2 and pX1x1…

Q: Suppose that the conditional distribution of Y given X = x is Poisson with mean E(Y|x) = x, and that…

A: d) From the given information, The conditional distribution of Y given X=x is Poisson distribution…

Q: Example 4.2. Suppose the joint distribution of X and Y is given by 1 P(X = x, Y = y) 42 (z + y°)…

A: Solution

Q: 5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the pdf of…

A: X is continuous uniform distribution in the interval (a,b). X ~ U(a,b) So, Variance of X, Var(X) =…

Q: In this question you are required to examine distribution at X(0) and x(1/8fo) x(0) ∈{0,-1 ,1}…

A: Given information: The distributions of X(0) and X(1/8fo) are given.

Q: 23. The continuous distribution of a variate X is defined by 0<x<1 f(x)= {(3-x), 2sxs3 Find the mean…

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Q: The random variable 'X' has the Poisson distribution Po(m) and P(X=5) = P(X=4) + %3D P(X=3). Find…

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Q: Let X denote the mean of a random sample of size 25 from the distribution whose pdf is f(x) = x²…

A: We have given that the X-bar denote the mean of a random sample of size 25 from the distribution…

Q: et X1,..., Xn be a random sample from a uniform distribution on the interval [20,0], where 0. et…

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Q: The joint p.m.f of (X,Y) is given by P(x, y) = 2x + 3y), x =,1,;02y = ,13,.2.Find the marginal…

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Q: If(x,y)-N(0-11,4,0.5),the marginal distribution of X~ Y₂

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Q: Suppose that a random variable X has normal distribution with mean µ = 2 and variance σ 2 = 9, that…

A: From the provided information,

Q: T has an exponential distribution such that P(TS2)=2P(T>4) What is Var(T)=

A: