a. If the probability density of X is given by 1 for 1

Q: Let S = {-1,0, 2, 4, 7}. Find ƒ (S) if a) f(x) = 1. b) f(x) = 2x +1. %3D c) f(x)= [x/5]. d)…

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Q: If A=A(t) find the A? m d²A RT da -3Tcr 2 dt dt

A: We have to solve the homogeneous solution first.

Q: Prove let B= 6+ I %3D : m = ',2,3, 3m S. Then inf(8) =6

A:

Q: c) Let S= {-1, 0, 2, 4, 7}. Find f (S) if i. f(x)=[x/5]. ii. f (x) =L (x² + 1)/3 %3D %3D

A:

Q: 2. A random variable X has pdf |x| < 1 elsewhere. cx(1+ x) a. Find c. b. Find E{X}and V AR{X} c.…

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Q: 11. The marginal density functions for independent random variables X and Y are g(x) and h(y). Find…

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Q: Let N1(t) and N2(t) be two independent Poisson processes with rates λ1=1 and λ2= 2, respectively.…

A: See the hand written solution

Q: . Find the expected value of the Probability density function: ƒ(x)= 24 (3x)(4 − x) - 64 on the…

A:

Q: 3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X²?. Y\X -2 -1 1 2…

A: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question and…

Q: If X has an exponential distribution, show thatP[(X Ú t + T)|(x ÚT)] = P(X Ú t)

A: Suppose X follows an exponential distribution with parameter λ. The RHS is given by:

Q: 1. Let x=(x) = (². Find xif 8. Exercise (2) ܘܚܢܟ b. x n

A: Given Data: Let us consider the given data, x=xn ∈l2. To Find: a. xn=212n b. xn=1n

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: (5)Find x if. i. e* = 3, ii. Inx = 2 iv. 32-x = 27, v. 8x+1 32. %3D

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Q: Let X be the number of times a fair die is rolled until one appears twice in a row. Find E(X).

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Q: Individual A has a red die and B has a green die (both fair). If they each roll until they obtain…

A:

Q: 1 (a) ƒ (kx) = 2x+1_2²²₂ = - 2*, x = 1, 2, ..., N, and zero elsewhere (b) f(x)=p(1-p)*, x=0,1, 2,…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted  # To…

Q: Let X have the following density. Values of X -2 -1 0 1 Probabilities 0.1 0.2 0.3 0.3 0.1 (i) Derive…

A: i) Formula for E(X): EX=∑XPX Consider, X -2 -1 0 1 2   P(X) 0.1 0.2 0.3 0.3 0.1   X*P(X) -0.2…

Q: Let X1,· , Xn be iid with pdf 1 -(x-01)/02, x > 01, -∞ 0. 02 f(x|01, 02) Show that (Xn – X1)/(X2 –…

A: Given that X1, X2, ...., Xn is iid with PDF, fx|θ1, θ2=1θ2e-x-θ1θ2,   x&gt;θ1 A statistics is…

Q: 2. Let f(x) = 3x(x² − 1)(x³ + 2x + 3) (a) Use distribution to expand the function. (b) Use the rules…

A:

Q: Let X have a Weibull distribution with parameters a and B, so E(X) = B· T(1 + 1/a) V(X) = B?{T(1 +…

A: Given information: The mean and variance of the Weibull distribution are given below:…

Q: Show that the autocovariance function can be written as γ(s, t) = E[(xs − µs)(xt − µt)] = E(xsxt) −…

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Q: b) Suppose that a sequence of mutually independent and identically distributed continuous random…

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Q: Suppose that  X and Y  have the following joint probability density function. f (x, y)  =  3x 400…

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Q: ASAP. Proof. LetXbea discreterandomvariable with probability functionpX(x);then…

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Q: 2. Let G = Z,xZ4, and find [G:H] for: a) H = {0}xZ4. %3D

A: We have to find [G:H]

Q: Find the largest and smallest distances between the point P(1, 1, 1) and the sphere x² + y? + z? –…

A: Given circle is x2+y2+z2-2y+6z-6=0, and P(1, 1, 1) Let C be the center of the circle.…

Q: (21) Let X b (12,5) find E(5+6x) and distribution function.

A: Given,X≈b(12,23 )E(x)=npE(x)=12×23 E(x)=8

Q: Consider the function [c(2x – x³), 0<z< fx(x) = |0, otherwise. Could fx(x) be a probability density…

A: From the given information, Consider, the pdf as follows: fXx=C2x-x3,  0&lt;x&lt;52…

Q: Find (i) P (X 0.3 ?

A:

Q: Consider the Prelec function w(p) = e−1.5(− ln p) . Consider only interior fixed points (so ignore…

A: Solution: Given:the Prelec function w(p) = e−1.5(− ln p)  fixed points w(0) = 0 and w(1) = 1).

Q: Let Xinexp(A). Sholw that T- Xi Sulficieay Statistics is

A: We will use the factorization theorem to determine the sufficient statistic.

Q: E[X] = 1 and Var(X) = 5, use definition of variance and properties of expectation to find (a) E[(2 +…

A: E[X] =  1  Var(X) = 5