2. A random variable X has the discrete uniform distribution i x=1,2,..., k, 10, elsewhere. f(x; k) = Show that the moment-generating function of X is e*(1 – e*t) k(1 – et) Мx() — |

Q: 1. Let X1, Xn be i.i.d. random variables with a pdf .... f(x) = = e-(x-0), 10, x > 0, elsewhere for…

A: The objective of the question is to compute the cumulative distribution function (CDF) of Y and Zn,…

Q: Let X1, X2,...,X, be a set of independent random variables each following the distribution with pdf…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (6) Let X be a Poisson random variable with parameter 0, then E(X²) = 1. От OF

A: Poisson distribution is the type of discrete probability distribution. It explain the number of…

Q: Q19. Two random variables X and Y have the joint pdf, fx y(x, y) = Ae-2x+y), x, y 2 0 = 0, 6. %3D…

A:

Q: (a) Is EX; sufficient for 0? (b) Find a complete sufficient statistic for 0.

A:

Q: (34) Let X be a random variable with p.d.f. 1<x<» k f(x) = { find k. O.w

A: Formula used: fx=x-2k           1&lt;x&lt;∞0                   Otherwise

Q: 36. Assume that X is a continuous random variable with pdf f(x) = exp [-(x + 2)] if -2 <x< o and…

A: Moment Generating Function (m.g.f.): Let X be a random variable with probability function…

Q: Let X be a continuous random variable with domain D = [0, 7] and PDF 0 <x < 2, 2 <x < 5, -ax + 7/10…

A: X = continuous random variable Domain [0,7] Pdf is given We have to answer for mentioned questions.

Q: ii) What is the value of the sample size n, if P[1(X₁ - X)² > 68.3392] = 0.025? i=1

A:

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)…

A:

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: If X be a continuous random variable with be -bx if x >0 f(x)= otherwise then the moment generating…

A: The random variables can be categorized into 2, continuous random variable and discrete random…

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

A:

Q: Q4) Assume that a variable x comes from a probability distribution of the form P(x|w) exp(Σwkf(x) 1…

A:

Q: Let xy X2 Xn be a random sample from a distribution ...... with p.d.f. f (x, 0)= e- (x – 0); 0< x< ∞…

A: ANSWER: Form the given data,

Q: (42) Let X be a random variable with p.d.f. ke 0<x<0 f(x) ={ find k. O.W

A: Given : f(x)=ke-23x                    0&lt;x&lt;∞

Q: 4. Let X be a random variable taking positive values and assume that E(X) exists. Which of the…

A: Option (I) is correct as E(X2)&gt;= (E(X))2 when we find Variance.

Q: (40) Let X be a random variable with p.d.f. (k +4)e¯3x f(x) ={ 01) O.w

A: a)Use the condition of valid pdf to find the value of k…

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: 2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following distribution…

A:

Q: (1) Let X = b(16,) find E(4-3x) and distribution function.

A: From the provided information, X~b (16, 1/4) Sample size (n) = 16 Probability (p) = 1/4

Q: 4. Let X and Y be independent random variables with gamma distributions, r(3,2) and I'(4,2),…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Let Y₁, Y₂, . . . , Yn denote a random sample from the uniform distribution over the interval [0,…

A: Given,a uniform distribution. .To,find a sufficient statistic for  and MVUE for .

Q: 2. Let U1, U2,... be independent random variables, each with continuous distribution that is uniform…

A: The problem can be solved using the concept of expectation and moment generating function.

Q: 1. Let X,,X,,.., be a random sample from a Geometric distribution fx(x) = p(1– p)* , x=1,2,3,... a.…

A: 1) X1,X2,X3.....,Xn are the identical independent random variables from geometric…

Q: A statistic is denoted by T(X1,.., X„) or simply T(X) 14.- Let X1, X2 be a random sample from the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: S(z|4, A) = () the statistics `X and 1=E in ent and complete. , show that X has an inverse Gaussian…

A: *Answer:

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

A: Solution

Q: Let X be a continuous random variable with PDFfx(x)= 8/x3, x> 2. Find E[W where W = X/3.

A:

Q: Let X1, X2,..., X, be a set of independent random variables each following the distribution with pdf…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Let X(1) 0. a) Show that X4) and X(6) – X() are independent for any s>r. b) Find the distribution of…

A:

Q: Suppose that X,, X2,...,X, denotes a random sample from a Poison distribution with mean 2. Find the…

A:

Q: (52) Let X be a random variable with p.d.f. 1 0<x<0 f(x) = ,find E(e") O.w -in

A:

Q: A random variable X has a pdf [c(1-x*) -1<x <1 fx(x) otherwise (i) Find C. (ii) Find P[|x|<1/2].

A:

Q: (40) Let X be a random variable with p.d.f. (k +4)e-3* f(x) =- 01) O.w

A:

Q: Ql: ) Let X1,X2, X3 and X, be four independent random variables, each with pdf f(x)=5(1-x)*, 0kx<l,…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the moment-generating function of gamma distribution to show that E(X)=a0 and Var(X)=a®² ||

A:

Q: 3.2.13 Y is a continuous random variable with { 2(1- y), 0< y < 1; fy(4) = { 0, otherwise. Derive…

A: Let Y denotes the Continuous Random variable. From the information, given that

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: (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: Let X,, X2, .. .be independent Cauchy random variables, each with PDF d f(x)= T(d² +x²)' Show that…

A:

Q: Consider the continuous random variable X whose pdf is given by f(z)=(a-³) LOSISI(I). (a) Find the…

A: Note: Hi there! Thank you for posting the questions. As there are multiple sub parts, according to…