Let X and X1, X2, ... be random variables. Then |Xn – X| 1+|X, – X| X, 4 X as n →∞ → E 0 as n → 0.

Q: Let X and Y be integrable random variables on the probability space (Ω,F,P)andA be a sub-σ-field of…

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Q: dp dq 2 if p = In(q7 + 7). Find dp dq ||

A: Simply use the chain rule of derivative and simplify.

Q: Exercise 1. Suppose t₁ (n) = O(n²) and t₂(n) = O(n²). Encircle in the following list all the…

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Q: Find ſ xJ3(x)dx

A: We will evaluate the required integral.

Q: Let X be a discrete random variable such that P(X = n) = (1 − p)"−¹p. Prove that E(X-¹) = -pln(p)…

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Q: var(û), if û = X1 + a jg X (n-1) + (X2 ++X(n-2) + 3 6X(m-1) + 증 .. 2(n-3) 4. 29n 256(п-3) 29…

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Q: Assume that Pr[E]=0.55, Pr[F]=0.55, Pr[G]=0.45, Pr[E∪F]=0.8,Pr[E∪G]=0.75, and Pr[F∪G]=0.75. Find the…

A: From the provided information, the known values are: Pr[E]=0.55, Pr[F]=0.55, Pr[G]=0.45,…

Q: If X1, X2, ... , Xk have the multinomial distribution ofDefinition 8, show that the covariance of Xi…

A: From provided information, X1, X2, … , Xk have multinomial distribution. A discrete k dimensional…

Q: 4. Let u = and v = and w = Compute (u x v) x w. %3D 3

A: u×v=ijk-211103=3i-j-6-1+k0-1=3i+7j-k now find u×v×w u×v×w=ijk37-1-111 =7+1i-j3-1+k3+7 =8i-2j+10k

Q: LetX bea discrete random variable withprobability functionp(x), g1(X),g2(X),g3(X),···,gk(X) be k…

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Q: 28. Show {Xn, n ≥ 1} are independent if o(X₁,..., Xn-1) || σ(Xn) are independent for each n ≥ 2.

A: Given::- Show (Xn, n ≥ 1} are independent if o (X1,..., Xn-1) || σ (Xn) are independent for each n ≥…

Q: Compute eAt where A =

A: We know that etA=∑n=0∞tnn!An So, we have to first find the value of An A1=1-1-11, A2=2-2-22…

Q: 2. Let X₁, X2, and X3 be independent random variables such that E(X₁) 6 Further, suppose that V(X₁):…

A: Let X1, X2, and X3 be independent random variables. 1. We have to Compute E(eX1X2+πX2X3+√19X3+3)2.…

Q: Derive recurrence relation 24,Cx)=スJ(x)+ x Jyni (x). Jy-i (x).

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Q: Show that 1 – R1.23 = (1 – r12²) (1 – r13,22 ) Deduce that (i) R, 23 2r,2, (ii) R? = r12² + r13², if…

A: Answer: For the given data,

Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: X = { 2,5,8,10}y and T= { 0, X, {5},{5,103} and T₁ = { 0, x₁ {2}, {5}, {2.5} let E1 = {2,83 and [2=…

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Q: 8 12 -4 -2 -5 12R 5R 11R 6R 3R 9R P(X=x) Evaluate R OA. 47 Ов. 1/46 OC. 1/40 OD. 40 OE. None of…

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Q: Let X(t) be a WSS random process. Show that for any a > 0, we have P{|X(t +T)= X(t)| > a} < 2Rx(0) -…

A: From the given information, X(t) be a WSS random process with parameters EXt=0 and RXτ. Consider,…

Q: Show that X is a random variable if and only if X¹([r, x)) = F for every reR.

A: A random variable is a measurable function of a probability space into a measurable space. This…

Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

A: From the given information, W follows normal distribution with mean µ=-1 and variance σ2=4.

Q: Let X and Y be random variables such that EX] = 2 and E[Y] = 3. a. Find E[4X +5Y]. b. Find E[4X – 5Y…

A: E(X}=2 and E(Y}=3 (a) E(4X+5Y)= ?  (b) E(4X-5Y+2)= ?  Farmula E(aX+bY+c)=aE(X)+bE(Y)+c

Q: Let vov1 ... V5 be a path. We fix an integer i, 0 <i< 5. Suppose that a person starts walking from…

A: Note: According to bartleby we have to solve the first question please upload the question…

Q: If X is uniform on [-2,2] then p(x <3) = 3/4 O O o o

A: Given  X~Uniform(-2,2) Pdf of X is  f(x)= 1/4     , -2&lt;x&lt;2       = 0         , otherwise

Q: If x is a random variable such that x-b(1,2) then P(V ( x) <x<E (x ) )is? X

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Q: If A%3 2x3 -Зх +2:х € [О, 2) then in (R, T,), A %3D а. [-3, 1] b. [-1, 1] с. [1, 3] С. d. [0, 4] e.…

A: Open sets and Closed sets: The sets in topology τ are called the open sets of the topological space…

Q: Suppose A E C such that X(2+i, 3 – i) = (5- i, 7- 5i). Then (1) A = (1– i) (2) A = (2– i) (3) Does…

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Q: Which of the following is a cube root of – 2.3 – j1.25 1.3782 + j3.3075 -1.3593 - jo.2276 -1.3782 -…

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Q: 3. Evaluate 26 tan xdx

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Q: Show that Σ dn o(n) n for every positive integer n.

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Q: fx,y (r, y) = %3D elsewhere be the joint probability function of the random vector (X,Y). Which of…

A: f(x,y) = 0.5ye^(-x)