If X is a continuous random variable find the CDF and density of the function y = x/3

Q: If X is uniformly distributed over (-1,1), find P(IX| > а. b. Density function of the random…

A: The given information is X~U[-1,1] a.…

Q: If the probability density of a random variable is given by 0<x<1 f(x) ={2-x 1<x< 2 0 elsewhere…

A: Given,f(x)=x0&lt;x&lt;12-x1≤x&lt;20elsewhere

Q: If a random variable X has a uniform density with theparameters α and β, find its distribution…

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Q: Consider two continuous random variables X and Y with joint density function 0,otheruise P(X>0.8,…

A: We know, fx,y=x+y,0≤x≤1, 0≤y≤10Otherwise Therefore, PX&gt;x, Y&gt;y=∫x1∫y1fx,y dy dx

Q: Suppose that the random variable X has density fx (x) = 4x³ for 0 4X).

A: Given the density function

Q: A random variable Y is defined as X3 Y = 2 - X² + 3 Find the density of Y.

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Q: Let X be a Gaussian random variable with zero mean and variance equal to 2. 1-Find the probability…

A: It is given that, X be a Gaussian random variable with zero mean and variance equal to 2. That is,…

Q: Let X be the random variable with the density function f(x) given by 2.2 3.2 if a >0 f(x) = (1+z)3…

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Q: Suppose that X and Y are random variables with the joint density function 1+ x - 5 4 |X<-4).

A: Let X and Y be two continuous random variables defined over the sample space S. Then the continuous…

Q: Suppose the random variable Y has an exponential distribution with mean 2. Use the method of…

A: The random variable Y has an exponential distribution with mean 2.

Q: 2. If a random variable X has a uniform density with the parameters a=4 and B = 5, find its Density…

A: A random variable X has a uniform density with the parameters α=4 and β=5

Q: the popularity density function f(x) for a uniform random variable X defined over the interval…

A: It is given that the variable X is uniform random variable with interval [2, 10].

Q: Suppose that the random variable W has a beta distribution with probability density function f (w)…

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Q: Give an efficient method to generate a random variable X having density f(x) = 1 ¤(1– x)*,0.8 < æ <…

A: Given that : f(x) = 10.000336x1-x3 , 0.8&lt;x&lt;1f(0.8)=10.0003360.81-0.8…

Q: Consider two continuous random variables X and Y with joint density function 0,0otherwise P(X>0.8,…

A: P(X&gt;0.8,…

Q: Suppose that the random variable W has a beta distribution with probability density function f(w)…

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

Q: If two random variables have the joint probability density s(*, x2) (* +2r2) for 0 < x1 < 1, 0<x2 <…

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Q: Let X be a continuous random variable where the density function is given by: (1x) 0 if-3<x<3…

A: Given information: fx=x9, -3&lt;x&lt;30 otherwise    =-x9, -3&lt;x&lt;0x9, 0&lt;x&lt;3Consider,

Q: A random variable X has the density function: fx (x) = { 3 (3-x) 1<x<3 10 otherwise

A: Consider, EX2=∫xx2fxdx          =∫01x2*65x2dx+∫133103-xx2dx          =65x5501+3103x33-x4413…

Q: Suppose that the random variable W has a beta distribution with probability density function f(w)…

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Q: The probabliity density function for the random variable X is given by x2. f(x) = {(25 - x2), 0, 0<x…

A: Given that ; Here a probability density function is given.  By using the concept of cumulative…

Q: Let X be a random variable having the density function, Find the variance of the random variable…

A: We have given that  Probability distribution function pdf. f(x) = x2/3   , - 1 &lt; x &lt; 2   I…

Q: A continous random variable has density function f(x)=(3x2)/(03) for Osxse, for some 0>0, and zero…

A: First we have to determine mode and median of given distribution.

Q: If X is a continuous random variable, then we know P(a≤x≤b) is equal to the area under PDF curve…

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

Q: Show that the mean value and variance of random variable having the uniform density 1 function,…

A: The probability density function of a uniform distribution is given below:

Q: The probability density function of a random variable Y is given by 24y(10+2y-0.3y) S,(y)= ,0<y<10…

A: Given information: a) Consider,   The probability that the sample sum T=∑yi  is between 200 and…

Q: Let X and Y be random variables with joint density function f(x, y) given below. Find P(X < µ2),…

A: Hi, you have posted two questions in one time. As per the guidelines I am obliged to answer first…

Q: The joint density function of the random varıables X and Y is 6-x- y 0<x< 1, 0 < y<1-x, f(x,y) = 8.…

A: From the given information, fx,y=6-x-y8, 0&lt;x&lt;1, 0&lt;y&lt;1-x

Q: If the random variable X · Exp(0), then what is the probability density ction of the random variable…

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Q: Let X and Y be independent exponentially distributed random variables with parameter X λ = 1. If U =…

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Q: Consider the random variable X with the uniformdensity having α = 1 and β = 3.(a) Use the result of…

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Q: Suppose that X is a random variable whose density function is defined as follows: (a+1) æª fx(x) =…

A: Given,fX(x)=α+1xα2α+1   ;  0&lt;x&lt;2for α=1.15f(x)=1.15+1x1.1521.15+1f(x)=2.15 x1.1522.15  ;…

Q: show how to generate random variables from a uniform density on an interval (a,b)

A: In the given problem we have to answer the question of, how to generate random variables from a…

Q: Find the characteristic function for a random variable with density functio: fr (x) = x for 0<x<1

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Q: The proportion of flour Panera Bagel Company uses each day can be explained by a random variable Y…

A: We have given that the probability density function of random variable Y and we need to find the…

Q: Find the density of Z = (X+ Y)2, where X and Y are independent uniform random variables over (-1,…

A:

Q: Let the density function of a random variable X be given by f(x)3 0x, 0SXS1 Compute the sufficient…

A: Given : fX(x)=θxθ-1 ; 0≤x≤1

Q: 3. If a dealer's profit, in units of $5000, on a new automobile is a random variable X having the…

A:

Q: Suppose that X is a random variable with probability density function given by: fx (x) = { k(x³ +…

A: To find k k∫02(x3+x) =1kx44+x2202 =1k164+42 =1k=16

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

A: Given, fx;β=xβ2e-βx, x&gt;0 Now the likelihool function is obtained as-…

Q: Find the expected value of the function g(X) = X³ where X is a random variable defined by the…

A: g(x) = x3 where X is a random variable defined by the density fx(x)  = (1/2)u(x)e-(x/3)

Q: If X and Y are independent random variables with common density f (x) = = for 0 < æ < 2 then (fx *…

A: Let X and Y be the independent random variables having common density  f(x)=x/2.    0&lt;x&lt;2 We…

Q: 4. The shelf life in days, for bottles of a certain prescribed medicine is a random variable having…

A: The probability distribution function is given by: Fx=20000x+1003x&gt;00,elsewhere So the…

Q: Find the density function of the random variable X if the characteristic function is Ør (@)…

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Q: If the density function of the random variable is be-bx, x >0, f(x)= 0, %D Otherwise.

A: The probability density function for X is,

Q: The expected values of the independent random variables x and y (E(x) and E(y)) for a joint density…

A: Given: E(x)=5 E(y)=6   x and y are independent random variable

Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X +…

A: 1] X is a normal random variable 2] μ=5 and σ=1 3] Y=X2-10X+25