: Let (X, r≥ 1} be the integer-valued identically distributed intervals between the times of a recurrent event process. Let L be the earliest time by which there has been an interval of length a containing no occurrence time. Show that, for integral a, E(s) = saP(X₁ > a) 1-1 s² P(X₁ =r)*

Q: Let the random variable X have the pdf f(x) = e-ª for 0 < x < ∞, and 0 elsewhere. Compute the…

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Q: The score on an exam from a certain MAT 112 class, X, is normally distributed with μ=81.2 and σ=10.…

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

Q: Let X1, ... , Xn be a random sample have the pdf 1 (1-0) f(x,0) = -(x),0 < x < 1, 0<0 < ∞. Find mle…

A: The likelihood of X1,X2,...,Xn is given as: L=∏i=1nfxi,θ=∏i=1n1θxi1-θθ=1θ∏i=1nxi1-θθ…

Q: Suppose that a continuous random variable X follows a uniform distribution over {-4, 4]. (a) Find…

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Q: The projection X of the radius-vector of a random point on a circumference of radius a onto the…

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Q: f(x) = log5 (2x + 1).

A: To  Determine:  Interval of convergence  f ( x ) = log5 ( 2x +1)

Q: (b). Use the definition of the derivative to evaluate f (x)=x". [Hint: Use the Binomial Theorem:…

A: Given: i. fx=xnii. a+bn=an+nan-1b+nn-12!an-2b2+·····+nabn-1+bn. To Find: Use definition of…

Q: Assume that X is uniformly distributed on the set S = {- 3, -2, -1,0,1,2,3}, that is, X assumes each…

A: Firstly list down the possible elements of y variable where  The set Y is obtained as: Hence the…

Q: If two balls are drawn without replacement from a bag with eight white and four black balls, what is…

A: GivenNo.of white balls in a bag=8No.of black balls in a bag=4Total no.of balls=12

Q: Q1)The function f(x)=x(x-6)^2 satisfies both hypotheses of the Mean Value Theorem on the interval…

A: Q1)The function f(x)=x(x-6)^2satisfies both hypotheses of the Mean Value Theorem onthe interval…

Q: Suppose f" (x) = N,(h) + a,h? + azh* + azhº + ... %3D The value of N2(h) using Richardson's…

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Q: If F(x) is cumulative distrbution function of a continuous random variable X, the probability…

A: False

Q: Let X ~ N(12, 5). Find the value of x0 such that (a) P(X > x0) = 0.05 (b) P(X x0) = 0.90.

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Q: Let U1, U2, ... be i.i.d. Uni(0, 1) random variables. - log U; is distributed as exp(1). (2) Find…

A: 1) From the given information,  U1, U2, ....... be i.i.d Uni(0,1) random variables. Given that…

Q: Let X be a symmetrically distributed RV with mean =0 It is known that P(X^2<1)=a, where…

A: Given information: Given that the random variable X is symmetrically distributed with mean 0.

Q: Let X be a continuous random variable described by f(x)=3(1- x)² for 0<x<1. Find The sketch a graph…

A: Given that, X be continuous random variable with Pdf given by, ,f(x)=3(1-x)2            ;…

Q: Suppose that the probability density function of x is (3x², 0 (2/3)) b) Determine the cumulative…

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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…

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Q: A bank teller series customers standing in the queue one by one. Suppose that the service time X,…

A: Answer: Using the given data,

Q: What is the expected duration (in days) of unemployment of the job-seeker? (Assume that the job…

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Q: For a random variable X, the "complimentary cumulative distribution function", or the "tail…

A: This question seeks to demonstrate that when a random variable X is either continuous or discrete…

Q: Let Y1,..., Yn be random sample from a Gamma (α, ẞ), show 1/nΣ1 Y² converges in probability and find…

A: denotes a random sample from a .It must be proved that  converges in probability and it's limit must…

Q: Let X1, X2, . .., Xn be a random sample from a population with a pdf a+2022 (a+ 2021) () ; х > 0, а…

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Q: Snowflakes land randomly on a small area of the ground at a rate of 16 per minute. Let X be the…

A: Solution

Q: Suppose f"(x) = N;(h) + a,h + azh² + azh³ + -…- ... The value of N2(h) using Richardson's…

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

A: Solution

Q: Consider the time series model x, = 0, +(1-0,B)z,, 2, - NID (0,02) Derive: b) the variance of x,. c)…

A: Given the time series model : xt=θ0+1-θ1Bzt ,  zt~NID0, σz2

Q: (a) P(2 < Xs 5), (b) P(3 < X s 7), and (c) P(X 2 6). *

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Q: x >1 f(x) =x10 xs1 ermine the value of k for which f(x) is a legitimate pdf. ain the cumulative…

A: Since the question has multiple sub parts we will solve the first part only.  Please resend the…

Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

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Q: a) Find P( X >28 ) use normal approximation to binomial with continuity correction  n=50 p=.8

A: Given that p = 0.8 and n =50.

Q: Find Var(X) if X is a Uniformly distributed b Binomially distributed C Normally distributed

A: Given: We need to find variance for- Uniformly distributed Binomially distributed Normally…

Q: The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp…

A: Thank you posting this question! Since it contains multiple sub-parts, as per the policy, I will…

Q: et X be the number of litres of milk shake that is requested at a café on a hot summer day. Assume…

A: According to question, we have to find c such that, P(X&lt;c) = 0.95. Using Ti-84 calculator, we…