3) Let X be a continuous random variable with PDF x20 fx(x) ={0 otherwise Find E[X], Var[X] and M (t) = E\ e* .

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: 2- Suppose = {xt)dt . Find ES and d acconding the statistical characteristics of xt).

A: For a continuous random variable X, a probability density function is a function such that (1) f(x)…

Q: 1. Suppose that the random variable X has the pdf given by T(a+B) pa-1(1 – x)ª-1 Г() f(x) = for 0 <…

A:

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 PDF 1 fx(x) for all a E R V27 and let Y = X². Find fy(y).

A: The PDF of X is fXx=12πe-x22, for all x∈ℝ Given Y=X2 We have to find the PDF of Y.

Q: Let X be a continuous random variable with probability density function 2x f(x; 0) = () e-²/0 for x…

A: Given density function of X is, fx=2xθe-x2θ, x&gt;0 Consider, EX2=∫0∞x2fxdx…

Q: 9) Let the continuous random variables X and Y have joint pdf f(x, y) = ex-y,0<x< 00,0<y < o, then…

A: NOTE*** As per bartleby guidelines for more than one question, only first to be answered send other…

Q: Suppose X~Uniform (0,1), and Y = -ln (1-x). (a). Find the probability density function of Y

A: Given that X follows Uniform distribution with (0, 1). Y=-ln1-X a) Consider, the cumulative…

Q: If X has a uniform distribution U(0, 1), find the pdf of Y = ex with ndf

A:

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

A:

Q: 21. Let X₁, X2, ..., Xn be a random sample from a population X with density function [0x0-1 for 0 1…

A:

Q: For a well behaved function, y = Ax(1-x) (where, 0) for a series of measurements of 'x'.

A: (i) Normalization constant…

Q: Let X be a continuous random variable with pdf f(x). If f(x) = 0 for x 0, P(X >a) < a where μ-…

A: Continuous Random Variable: A continuous random variable is a variable whose value can be obtained…

Q: 9. Let Y1, Y2,..., Yn constitute a random sample from the pdf given by f (v) = (0 – y) for 0 sy sO.…

A: Given: The sample probability distribution function of Y1,Y2,......Yn is: f(y)=2θ2θ-y  for  0≤y≤θ

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: 11) If X be a r.v. from exponential distribution (x)= e- ス>0, x20 Then the moment generating…

A:

Q: Suppose that two continuous random variables X and Y have joint probability density function fry =…

A: From the given information, c.

Q: Suppose X1 and X2 are iid observations from the pdf f(r|a) = ax 0. Show that (log X1)/(log X2) is an…

A:

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

A:

Q: Find the maximum likelihood estimator for θ in the pdf f(y; θ) = 2y/(1 − θ^2), θ ≤ y ≤ 1.

A:

Q: Let X be a random variable with the gamma probability density function. Derive the MSE of T=X2+2X

A: Gamma distribution: It is a continuous random variable, with the probability density function of…

Q: 4. Let X be a single observation from a Bernoulli density. Let T₁ (X) = X and T₂(X) = a. Are both T₁…

A: Given:Let X be a single observation from a bernoulli .T1(x)=X and T2(X)=12

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

A:

Q: LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the…

A: It is known that E(Xi) =1/λ and Var(Xi) =1/( λ2) EY=EX1+X2+...+Xn         =EX1+...+EXn…

Q: A2. Suppose that the continuous random variable x has the probability density function 1 f(x) -…

A:

Q: Suppose that a random variable X has a continuous distribution with the probability density function…

A: Answer:-  Given X has a continuous distribution with the probability density function…

Q: Q2- Let random variable X has the following PDF 2х 0 < x < k f(x) = }k2 О.w find k such that Var(3X)…

A: Given: fx=2xk2        0&lt;x&lt;k0            otherwise Var (3X) = 2

Q: Let X1,., X, denote a random sample from the probability density function f(r) = 0x-1, 0 0. Show…

A:

Q: The Exponential pdf for continuous random variable Y takes the form y > 0 fV) = for B > 0. y 2+t|Y…

A:

Q: 2. Let X be a continuous random variable with density function f(x)= for 0≤x≤2 0, otherwise Find…

A:

Q: If X1,..., Xn is a random sample from a distribution with pdf 303 x E R+, 0 E R+ f(x; 0) = { (z+0)4…

A:

Q: If X is an exponential random variables with rate 1, then its distribution function is given by…

A: Here it is given that , F(x) = 1 − e−x Let us consider , F(x) = u. Now the distribution function…

Q: 2. Suppose X is a continuous random variable with pdf -즐z if 0 1.0).

A:

Q: Let X be a continuous random variable with the following PDF fx(x) = - 0, x 20 x< 0 where c is a…

A: Given: fxx=ce-x,x≥00,       x&lt;0

Q: let X and Y have the joint density e-(x+y) for 0<x,y<∞ f(x.y)= other wise then X and Y are…

A: Solution: From the given information, the joint density function of X and Y is

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: Example 25: Let X be a uniformly distributed random variable in the interval (- T, T). This…

A:

Q: f x is a random variable with a probability density function defined by he form x20 , f(x) = 2xe¬x…

A: Solution

Q: Let X and Y be jointly continuous random variables with joint PDF is given: f X,Y (x.y) (1+x²y)…

A:

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: Let X denote the temperature at which a certain chemical reaction takes place. Suppose that  X has…

A: Given : Pdf of X : f(x) =194-x2     -1≤x≤20                       0.w

Q: Let X1, X2, ..., Xn denote a random sample from the probability density function fx(x) = ax for x E…

A: Given : fX(x) = αxα-1    for x ∈(0,1) and  α&gt;0.

Q: 1. If X is a continuous RV having distribution function F(x) (i) Find the PDF f(x), (ii) Find P {X >…

A: Given Cdf  F(X)=1-e-2x if x≥0

Q: 1. Let X and Y be two jointly continuous random variables with joint pdf f(x,y) = {k(x + y), 0≤x≤…

A: Given that                      We have to find  Var(X)  And  P(1/2&lt;X&lt;1, 0&lt;Y&lt;1/2)

Q: If X and Y are continuous random variables such that Y|X = x is uniformly distributed over [x, x +…

A:

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: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

A:

Q: Let X1, X2,..., X, denote a random sample from the probability density function fx(x) = axa-l for r…

A:

Q: Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF,…

A: It is given that the X is a continuous random variable with pdf f(x) = c( 25 -x2 ) , − 5 ≤ x ≤ 5 ,…

Q: .Let X be a random variable with the gamma probability density function. Derive the MSE of T=X² +2X

A: Here, X~Gammaθ,n,n&gt;0,θ&gt;0 and T=X2+2X

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.