Let X1, X2, Xn be a random sample from a distribution that has pdff(x,0) = e2 x e-8x x20 where 0 is an unknown parameter, then the MLE for 0 is

Q: Let X and Y be two independent random variables with PDFS fy (x) = with x>7 and fy(y) = 1Ry with…

A: From the given information, f(x)=98x3, x>7f(y)=118y, 0<y<6 Consider, E(X)=∫7∞xf(x)dx…

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: The joint pdf of a bivariate random variable (X,Y) is given by ke-(ax-by) x>0, y>0 fxy(x,y) = 0…

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Q: probability

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Q: Consider an i.i.d sample of random variable with pdf f(x) = 1 0<X < 0 + 1 then the method of moments…

A: Given functionf(x)=1  ; θ&lt;x&lt;θ+1

Q: Let Y1 &lt; Y2 &lt; · · · &lt; Yn be the order statistics of a random sample of size nfrom a…

A: The pdf of kth order statistic is as follows: fyk=k×nCkf(y)Fyk-11-Fyn-k

Q: Let X1,..., Xn be a random sample from a uniform distribution on the interval [20,0], where 9 0. Let…

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Q: Let X be a normal distribution with mean u and variance o? i.e. X ~ N(µ, o²). If Y = ex, then find…

A: 1. Given that Y=eX. Consider, the CDF of Y is, F(Y)=P(Y≤y)       =P(eX≤y)       =PX≤ln y       =ϕ(ln…

Q: Let X1, X2, ..., Xn be a random sample from a distribution that has pdff(x,0) = e² x e-8 is an…

A: Given pdf is, fx,θ=θ2e-θx, x≥0 Consider, the likelihood function, L=∏i=1nfx,θ  =∏i=1nθ2e-θx…

Q: Q3 Let X be a continuous random variable with PDF S 4x³ px(x) = 0 < x < 1 otherwise Find E(X) and…

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Q: Let X and Y be two continuous random variables with joint probability density 3x function given by:…

A: We know that, Var(X)= E(X^2)-(E(X))^2 so from the given values, = (3/5)-(3/4)^2 = 3/5 -9/16 =…

Q: Suppose two random variables X and Y are independently distributed as Unif(0, 1). Let D = Y – X, Z =…

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Q: The Gamma pdf for continuous random variable Y takes the form 1 va-le-y/ß -lB y > 0 f(y) = βαΓ (α) "…

A: Given that Y has Gamma distribution with α=3 and β=1.6. Consider,…

Q: Suppose the random variables X and Y have a pdf given by f (x, y) = kæy on 0<x<1,0<y<1 Find k.

A: 4.

Q: Let X,, Xy, .X, be a random sample of size n from the exponential distribution, Exp(8), with an…

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Q: 17. The diameter of electric cable, say X, is assumed to be a continuous random variable with pdf:…

A: Given f(x)=kx(1-x) ; 0≤x&lt;1

Q: Let Y1, Y2, Yn be a random sample from a Gamma distribution with parameters a = 1 and ...) B = 0 >…

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Q: Consider a random sample X1,..., Xn with n> 3 from the exponential distribution with parameter > 0…

A: Given that  X1,X2,......Xn with n&gt;3 from the exponential distribution with parameter λ&gt;0 and…

Q: 9. Let Y1, Y2,., Yn denote a random sample from the probability density function given by 0-1 0<y<3…

A: Solution:- Given that pdf of y f(yθ) = θ yθ-13θ , 0 ≤y≤30 , elsewhere

Q: Let X1, X2,..., Xn be a random sample from a population with probability density function s(2) =…

A: The method of moment estimator is found using the kth theoretical moment of a random variable, hence…

Q: Consider an i.i.d sample of random variable with pdf f(x) =1 0<x<0 + 1 then the method of moments…

A: In method of moment estimation we equate population moment with sample moment. Now, first order…

Q: Let X1...,Xn be independent random variables where each X; has a pdf f(r; 0) = 0x°-1 for 0 0 is an…

A: In such type of problems, we first attempt to find the asymptotic distribution of sample mean, X¯…

Q: 3. Let X and Y be continuous random variables with joint PDF S3x 0<y<x<1 f(x,y) = otherwise…

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Q: The joint PDF of the random variables X and Y is defined as f(x, y) = 25e: 00 = 0, otherwise (i)…

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Q: Let X1, X,... An be a random sample from a distribution with pdf f(x.p) = p(1-p)' where 0<p<5 is a…

A: In the given problem sample size n is not given hence I have taken n=19  to find probability of type…

Q: Suppose that independent observations a1, r2,...,n are available from the log-normal distribution…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let X be the random variable having pdf f(x) = 1,0 < x < 1, zero e.w. Compute the probability of the…

A: Give X~U(0,1)  P(X(4)-X(1)&lt;1/2)= ?

Q: Let (X1, ., Xn) be a random sample from the following discrete distribution: 2(1 – 0) P(X1 = 1) =…

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Q: Suppose X and Y are continuous random variables such that the pdf is f(x,y) = x + y with 0 < x < 1,0…

A: Given information: The joint probability density function of two continuous random variables X and Y…

Q: Let X1, X2, ... , Xn be a random sample with pdf f(x) = (0+1)xº-1, 0sx<1,

A: Given information: f(x)=θ+1xθ-1, 0≤x≤1, 0&lt;θ&lt;∞ Consider, the likelihood function, Lx=∏i=1nfx…

Q: For a random variable (X) having pdf given by: f(x) = (k)x^3 where 0 ≤ x ≤ 1, compute the following:…

A: Given,f(x)=kx3  ;  0≤x≤1

Q: Let (X,Y) be a two-dimensional random variable with the joint pdf {6xy 0<x<1,0 < y< Vx otherwise…

A: The given probability density of (X,Y) is given as, f(x,y)=6xy ; 0≤x≤1, 0≤y≤x0     ; O.W   Need to…

Q: If f(x) = e-& ; 0 3) —

A: Given,f(x)=e-x ;0&lt;x&lt;∞

Q: The Exponential pdf for continuous random variable Y takes the form e/ß y > 0 fV) = for ß > 0. y < 0…

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Q: Let X1, X2, ...,Xn be a random sample of size n from a distribution with probability density…

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Q: Let X1, X2 be a random sample of size n : = 2 from the exponential ity function (pdf with an unknown…

A: Given information: Given that the random sample X1, X2, … ,Xn is from an exponential distribution…

Q: Let X1,, X, be a random sample from a population with pdf (0 + 1)r", if 0 <r<1 fe(x) = 0, %3D…

A: Given information: Let X1, X2, …, Xn is a random sample of size n taken from a probability…

Q: Let X1, .., X, be a random sample with pdf defined as: 2x f(x) = Aexp{- x²/0}, where 0 > 0. The…

A: Given information: The probability density function of a random sample X1, X2,…, Xn is given below:

Q: If X₁, X₂, ..., X is a random sample from the population with E distribution (4,0) with density…

A: 3. From the given information, the density function is, fx|θ=16θ4x3e-xθ, x&gt;0 Consider, the…

Q: 3) Let X be a continuous random variable with PDF 1 x20 fx(x) ={0 otherwise Find E[X], Var[X] and…

A: Let X be the continuous random variable with pdf, fX(x)={1θe-xθ; x≥00; otherwise To find E[x],…

Q: Let X1, X2, ..., Xn be a random sample from a distribution that has pdf f(x,0) = 02 x e-ex x unknown…

A: Given: The pdf given is as follows fx ;θ=θ2×e-θx    x≥0 n samples are drawn

Q: Let X and Y be two jointly continuous random variables with joint PDF x + y 0 < x, y < 1 fxx (x, y)…

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Q: Let X and Y be random variables with joint pdf 8xy for 0 fx,y (x, y) where k is a positive…

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

A: Solution

Q: der a random sample X1, X2, ..., X, having the pdf, f(r; 0) 1<I<1, -1<0<1. Show that 0 = 5X is an…

A: Solution: From the given information,

Q: 3. Let X1, * , Xn be a random sample. Find the mlle of 0 for the cases that the population pdf/pmf…

A: We want to find the MLE of theta1 and theta 2

Q: X is a random variable that has the following PDF function: fx(x) = 0.28(x + 2) + 0.38(x + 1) +…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let X be a random variable with pdf given by f(x) = 2x for 0 1/2). b. Find P(X > 1/2|X > 1/4).

A: The given pdf is fx=2x for 0≤x≤1 and fx=0 otherwise.

Q: Let X, and X, be independent exponential random variables having pdfs f, (x1) = e=, x > 0 and…

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!