Consider the Parcto distribution with Cumulative distribution func- tion: (G)". F(X) = 1 Compute its probability (density) distribution. Conmpute the variance. Under which condition on 3 is the variance finite?

Q: Let X1, X2, X3, X4 be a random sample from the distribution with PDF f(x) = e¯, x > 0. Calculate the…

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Q: Suppose X is a Poisson random variable with rate parameter A, where A is a random variable itself…

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

Q: Suppose X is a random variable taking values in the interval [0,2] with probability density function…

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Q: A pumping station operator observes that the demand for water at a certain hour of the day can be…

A: The objective is to find out the max. capacity of water when demand follows exp. dist. with mean…

Q: Find the probability that the range of a random sample of size 4 from theuniform distribution having…

A: Given: Sample size, n=4 f(x)=1,   0<x<1

Q: Let X, and X2 be independent random variables, each having a standard normal distribution. Show that…

A: From the given information, X1 and X2 are independent random variables each having a standard normal…

Q: Find the uniform distribution of the continuous type on the interval (b, c)that has the same mean…

A: Given information is,  b+c2=8b+c =16c-b212=16c-b2=16×12c-b =83

Q: Let X be distributed according to a normal law with mean µ = 0 and unknown variance o². Find o?…

A: We have to find variance.

Q: If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean…

A: Solution: From the given information, the probability density function of X is

Q: A continuous random variable is said to have a Rayleigh distribution with parameter o if its PDF is…

A: Rayleigh distribution: A continuous random variable X is said to follow a Rayleigh distribution with…

Q: 2. Show how the Poisson distribution -m m e (x= 0, 1, 2,...) %3D х! can be regarded as the limiting…

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Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: Verify that if X has an F distribution with ν1 andν2 degrees of freedom and ν2 →q, the distribution…

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Q: Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2…

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Q: A variable has uniform probability density function between 1 and 2. What is the expected value of…

A: Given: X~U(1,2) a=1 b=2

Q: Let the random variable X fit the binomial distribution with parameters (p,N). Find the variance by…

A: Solution : Given : X ~B(p, N) where, p = probability of success N= no. of trials x = no. of…

Q: Consider the Pareto distribution with Cumulative distribution func- tion: F(X) = 1 – x > 1 Compute…

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Q: ibution formula. (b) using the normal approximation with

A: A fair coin is to be tossed 20 times n=20. P(Heads)=0.5 P(Tails)=0.5 total possible no. of…

Q: 1. Explain how to generate a random variable X distributed as the Cauchy distribution, whose…

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Q: Let f(x) be the pdf of a normal random variable with mean u and variance o?. Find the exact value of…

A: It is an important part of statistics. It is widely used.

Q: Let Y be a random variable with pdf giyen by

A: Given that fy=30y21-y2, 0&lt;y&lt;1 Formula for Ey4 is, Ey4=∫01y4fydy

Q: 2. A system consisting of one original unit plus a spare can function for a random amount of time X.…

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Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

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Q: Find the mean and variance of the Bernoulli distribution using the formula for the moment and…

A: Given that  We have to find the mean and variance of Bernoulli distribution using moment generating…

Q: Suppose that the unknown X is uniformly distributed between 0 and 1.  What is the expected value of…

A: Given: X is distributed uniformly between 0 and 1 a=0 and b=1

Q: 3.For the continuous random variable X with probability density function defined by ¤(2 – x) 0 <x <…

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Q: Let X be distributed according to a normal law with mean µ = 0 and unknown variance o². Find o?…

A: Given that X follows Normal(mean = 0, variance), then Z = (X - mean)/SD follows N(0,1)

Q: Is the graph shown a probability distributión (prob density function) of a continuous random…

A: Subject to validation of certain assumptions, a graph can be termed a probability mass function or…

Q: 5. Suppose that a continuous random variable X has PDF (1 – x²) -1< x<1 f (x) = else (a) Determine…

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Q: for the binomial distribution with n=24 and p=0.6, state whether or not it is suitable to use the…

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Q: Suppose that X1,.…,X, is a random sample from the Gamma distribution with density f(x; a, B) = r(a)…

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Q: Find the probability Pr⁡( Z ≤ 2.054 ) using the Standard Normal distribution (μ=0, σ=1) and also…

A: Given: Pr( Z ≤ 2.054 )

Q: Consider the distribution of Binomial, Poisson, Exponential, Gamma, and let T=X+ 4 & T, = (X- 1).…

A: An estimator is said to be unbiased if E(Statistic)= Parameter If not so  Then the estimator is…

Q: Suppose that X1, X2, ..., Xn and Y1, Y2, ., Yn are independent random samples from populations with…

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Q: The probability distribution of X, the number of imperfections for every 10 meters of a synthetic…

A: Solution-: Let, X-The number of imperfections for every 10 meters of a synthetic fabric  We have…

Q: Assume that X donotos the continuous random varlable with probability distribution of y & (A) and…

A: Basic probability

Q: Given an n dimensional random sample X from a population with density f(x, 0). Show that maximizing…

A: We know that the fuction x↦ln x is strictly increasing. Let θ' be the value maximizing Lθ/x and θ''…

Q: Let X be Bernoulli random variable, find the moment generating function X and find its mean,…

A: The answer is given using the concept of the Bernoulli random variable.

Q: Let X be a continuous random variable that is normally distributed with mean, µ = 15 and standard…

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Q: Let X1, X2, .. X50 be a random sample of size 50 from a distribution with density for 0 <x < o0 f…

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Q: Show that the characteristic function of a random variable having the binomial density is x…

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Q: Q1. If Var(X)=3, what is Var(2X + 1)? Q2. Compute the variance for a uniform random variable with a…

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