Q.2 Find the probability generating function of :1) P(X=2n) 2) P(X

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=. , find k. O.w

A: Step 1: Given,                            f(x) =1k e-8x0, 0&lt;x&lt;∞ We know that ,…

Q: 4 The continuous random variable X has p.d.f. f(x) where for -3 2.5)

A:

Q: 7) The discrete random variate X has the following pmf: 1 2 3 4 f(i) 0.2 0.35 0.2 0.15 0.1 Find the…

A: Given: The pmf of X is as follows i f(i) 0 0.2 1 0.35 2 0.2 3 0.15 4 0.1 Y=eX

Q: Y:PVI ZV. OA aill Asiacell 1/3 أحصاء امثلة.pdf Out come H. H=1/2 HH=1/4 H=1/2 -H T=1/2 T. HT=1/4…

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Q: 2/(a) Let X be a random variable with p.d.f. 1<x<0 S(x) = { find (1)k (2) Var(x).

A: Solution

Q: Q4: For the continuous probability function f(x) = 2kx²e-* when x > 0. Find a. Value of k %3D b. b.…

A: The definition of Gamma Function is given by, Γn = ∫0∞xn-1 e-x dx For any integer n,  Γn = (n-1)!…

Q: B. Let X and Y be random variables and let A e B. Prove that the function

A: SOLUTION ;

Q: Let X be a random variable such that E(X) = 3 and E(X') = 13. Use Chebychev's inequality to…

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Q: 12. Find the moment generating function of the random variable X, having p.d.f. х, for 0<x<1 f (x)…

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Q: X is a continuous random variable having p.d.f. f(x) such that f(x) = kx2 Osxs5 otherwise Find : (a)…

A: According to our guidelines we can supported to answer only first three subparts   Given

Q: (2) The two basic SDEs. Solve the following SDEs and find the expectation and variance of X4. (i)…

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Q: 12. Let a random variable X has a geometric distribution with p.d.f. f(x) = pq*", k =1,2,3,. Show…

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Q: 2) Let X₁, X₂, X3,... be a sequence of independent and identically distributed Bernoulli random…

A: As per bartlby guidelines we can answer only first question and rest can be reposted

Q: (30) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) = { , find E(e*) O.w

A: It is given X is a random variable with pdf f(x) = 2e-2x,0&lt;x&lt;∞0,otherwise

Q: (4) Let X be a random variable with p.d.f. 2e-2x 0 <x<0 f(x) =• find E(e-2x) O.W

A: Provided probability density function is, fx=2e-2x         for 0&lt;x&lt;∞=0…

Q: (27) Let X be a random variable with p.d.f. 3e-3x 0 <x< 00 f(x) =. , find E(x) O.W

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Q: Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

A: We have given two chi square distribution and we have to find the mean of  resultant F distribution.

Q: (13) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) ={ , find E(e2*) O.W

A: Solution :  Given :  f(x) = 2e-2x    0&lt;x&lt;∞0   o.w     E( e-2x )  = ∫x e-2xf(x) dx…

Q: 1. For any random variable X for which E(X) and E(X²) are finite, show that Var(X) = E(X²) – [E(X)]²…

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Q: (20) Let X be a random variable with p.d.f. 1 3 e - - X 0 <x<0 - k f (x) = find k. O.W

A: The p.d.f. is given by To evaluate : The value of k

Q: O Let X be a Poisson random variable with parameter 0, then E (X²) = 1 .

A:

Q: (b) Let X be a random variable with p.d.f. 2e 0<x<0 f(x)=< find (1)E(x) (2) Var(x) O.w

A: Given information:  X be a random variable with probability density function: fx=2e-2x…

Q: Q1/ Let X be a random variable having P. m. f ? P,(X) 1-find C.d.f. of X? 2-Graph the C.d.f.?…

A: Given information: X is a random variable with the probability distribution table as: X 0 1 2 3…

Q: 1. Under Ho, the likelihood function is given by L(Î.) %3D A. True O

A: Let xi; (i=1,2,...,m) be a random sample of size m from a population with probability density…

Q: Q2/(a) Let X be a random variable with p.d.f. kx 1<x<∞ S(x)=• find k. O.w

A: The p.d.f of X is given below: fx=kx-2   1&lt;x&lt;∞0          ow

Q: Let Y₁ 1 X=(x,-X₂), where X, and X₂ are independent random variables and each of them is distributed…

A: Given that the independent random variables X1 and X2 follows χ22 distribution.

Q: 4. The moment-generating function of a random variable X is est – e4t M(t) t + 0, and M(0) = 1. 4t…

A: Solution

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=- , find k. O.w

A: Given: The probability density function of the random variable X is given as:…

Q: (24) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) =- , find E(e³*) O.w

A: Here,Ee5x=∫0∞e5xfxdx=∫0∞e5x2e-2xdx=2∫0∞e3xdx=2e3x30∞=23e3x0∞=23e3∞-e30=23∞-1=∞

Q: 2. Let X be a discrete random variable whose range is the nonnegative integers. Show that E[X]=…

A: # discrete random variable x with non negative integers  Then to prove that E(x)=sum(1-F(x))  F(x)…

Q: (4) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x)= , find E(e2x) O.w

A: Random Variable: A random variable is a real valued function that assign a real number to each…

Q: 1. What is the expectation of the function g(x1, x2) = x, using the following joint PMF? %3D X1 3 6…

A: The given function is gx1,x2=x1.

Q: (a) Let X be a random variable and c is an arbitrary constant. Determine the value of c which makes…

A: Dear students as per guidelines we answer the first question only when multiple different question…

Q: Let X₁ and X₂ be the payoffs of two investments with E(X₁) = E(X₂) = 10. The expectation of the…

A: Given, X1 and X2 be the payoffs of two investments with EX1=EX2=10.

Q: (1) Let X be a random variable with p.d.f. -8x 0<x<0 k f(x)=< , find k. O.w

A: Given information: It was stated that X is a random variable. The probability distribution…

Q: (1) Let X be a random variable with p.d.f. e 0<x<0 k ƒ(x) = < find k. O.W

A: Let X be a random variable with pdf  fx=1ke-8x        0&lt;x&lt;∞0                         otherwise…

Q: 3. Let X, X,, X, be i.i.d. Exp(k) where 2= 1/10,000 hours. Assume X, represents the life of an…

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Q: Q2/(a) Let X be a random variable with p.d.f. -2 kx 1<x<0 f(x)=< find k. O.w

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: a) b) c) Show that for any &> 0 and S, ===₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1110 Show that a statistic…

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

Q: (b) Let X be a random variable with p.d.f. 2e-2x f(x) =• 0<x<0 find (1) E(x) (2) Var(x) O.W

A: Given the random variable X with p.d.f as fx2e-2x                  0&lt;x&lt;∞0…

Q: See picture please.

A: Given Moment generating function as shown below.According to defination of moment generating…

Q: The moment-generating function of the discrete random variable X is 1 M(t) =e 1 1 +. -2t 2t -3t e+…

A: Given that the Moment generating function of X is,

Q: Suppose X is a discrete random variable with pmf defined as p(x) = log10 fo x = {1,2,3,...9} Prove…

A: A pmf is legitimate if (i) 0≤P(x) ≤1                                   (ii) ∑P(x) =1

Q: b. Let X and Y be discrete random variables with joint probability function, f as follows, Y = 0 Y =…

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Q: (20) Let X be a random variable with p.d.f. 2 1 3 e -- 0<x<∞ k f (x) = find k. O.W

A: Given,f(x)=1k e-23x       0&lt;x&lt;∞

Q: Theorem 11. Let X be a random variable and let g(x) be a non-negative function. Then for r > 0,…

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Q: 4. Assume that X is an exponential random variable. Suppose further that Var(X) 5- E(X). (a) Find…

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