A random variable X has probability density function (pdf) fx(x), where   fx(X)= c(1–x4) -1≤x≤1 i) Find P [│X│ < 1/2]

Q: Does fxy(x,y) = $2; x> 0,y > 0,x+ y < 1 е. w. can serve as a joint probability density function of a…

A: It will serve as a joint Probability density function of a pair of continuous random variable x and…

Q: The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has…

A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…

Q: (a) Let the random variable X have a continuous distribution with the probability density function…

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Q: Find the conditional expectation E(Y/X=0.47) if the joint probability density function of the random…

A: We want to find conditional expectation.

Q: 1) Let X₁, X₂, X3....X₁ be a sequence of independent and identically distributed with the following…

A: Given X~N(mean=θ, variance σ 2=1)

Q: If X is the continuous random variable whose probability density function,Finc P(X=2) for 0≤x≤4 f(x)…

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Q: 1) The probability density function of X is: f(x) = 4xe-2x x>0 Calculate F(5) = ? where F indicates…

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Q: Two random variables X and Y have a joint cumulative distribution function given by FXY(x, y) = 1/2…

A: Define two cummulative distributions functions such that: F1(x) = 12u(x-2) + u(x-3)=0if x&lt;212if…

Q: A random variable X has the probability density fundion 1 x,2 < x< 5 5 1 5-x,5 < x <8 f(x)= - 0,…

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Q: Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise…

A: Given data: To find:

Q: a) Suppose that, for-1 ≤ a ≤ 1, the probability density function of (X₁, X₂) is given by f(x₁,x₂) =…

A: Solution

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

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Q: Determine E(X), E(X2) and V(X) if X be a continuous random variable with probability density…

A: The pdf of X is fx=3x2,0≤x≤1 EX=∫01x*fxdx=∫01x*3x2dx=3∫01x3dx=3 x4401=3144-0=34=0.75

Q: Find the mean and variance for the distribution of random variable X whose density function is f(x).…

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Q: Let X be a continuous random variable with probability density function 2x f(1; 0) = () -x² /0 for x…

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Q: Suppose that a > 0 is a constant. Let the joint pdf of random variables X, Y be fx,Y (x, y) x > 0, y…

A: To determine the value of the constant a, use the fact that ∫-∞∞∫-∞∞fx,ydydx=1. The conditional…

Q: A random variable X has the probability density function given below (2x, 0<x<1 g(x)={6+4x 1sx<3 0,…

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Q: Two Random Variables X And Y Have The Following Joint Probability Density Function (PDF) fxx (x,y) =…

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Q: et the density function of a random variable Xt fx(x) = Ox®-1, 0sxs1 0<x<1 ompute the sufficient…

A: The pdf of random variable X is given: fX(x) = θ xθ-1,   0≤x≤1

Q: Suppose that two continuous random variables X and Y have a joint probability density function f(x,…

A: Since you have posted a question with multiple subparts, we will solve first 3 subparts for you. If…

Q: 1. The random variable Y = X² does not have a normal distribution because the 1 2 e 1 probability…

A: Given that,  X~ N(u, σ2) Where u is mean and σ2 is variance. P.d.f of X,  f(x)=…

Q: A random variable X has a continuous distribution with a parameter d> 0 and the probability density…

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Q: If the probability density function of a continuous random variable X is [.5x 0< x<2 f(x)= otherwise…

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Q: If the joint probability density function of two continuous random variables X and Y is given by f…

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Q: The proportion of people who respond to a certain​ mail-order solicitation is a random variable X…

A: Given f(x) =23(x+1),    0&lt;x&lt;10,    elsewhere Since   σ2=E[X2]-E[X]2       E[X]= ∫01x.f(x)dx…

Q: b) Find the marginal probability density function of X, fy(x).

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Q: Find the expected value of the function g(x) = x°, where x is a random variable de- 1 fined by the…

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Q: 1. Suppose that for a certain life the probability density function is fx (x) = 1+x ,x >0 Find (i)…

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Q: A random variable X has a probability density function 0; x < 0, 0≤x≤1, 1<x<∞0. f(x)= { 22

A: a) Given information: fx=0, x&lt;012, 0≤x≤112x2, 1&lt;x&lt;∞

Q: Let X be a continuous random variable whose probability density function is: f (x) = 3x² for 0 <x <…

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

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Q: a) Suppose that, for -1 < a < 1, the probability density function of (X₁, X₂) is given by f(x₁, x₂)…

A: Solution

Q: 3. Let X be a continuous random variable with PDF: f(x) = 2x/9 for 0<x<3. Let Y = 2X+1. Using the…

A: As p[er the company rule, we are supposed to solve one problem from a set of more than one problem.…

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: (a) Let the random variable X have a continuous distribution with the probability density function…

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Q: A continuous random variable X has the following density function, * find the expected value of…

A: This can be solved using expectation formula

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Given: ƒ(x) = kx3; [2, 4] A probability density function equals 1 for sum of all range of values.

Q: Example 1 Let X have the probability density function 2x ,0<x<k f(x) = {kz 0 ,e.w. For what value of…

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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: 1. The proportion of people who responded to a certain mail-order solicitation is a (2(x+2) 2,0 <x<1…

A: HERE AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION  here given pdf of x

Q: B) The probability density function for the random variable X is given by 0<x<3 f(x) ={(25 – x²), 0,…

A: Given function is,  f(x)=x2, 0&lt;x&lt;3(25-x2), 3≤x&lt;60, otherwise

Q: The probability density function of a random variable is kx3 f(x) = if 0 <x< 2 V25 – x2 = 0…

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Q: 2x A random variable X has the density function f(x)= } k- 0, Otherwise. For what value of k the…

A: The given probability density function is as follows: The variance of X is equal to 2.

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: b. The random variable X has probability density function, ƒ given by { #(1+x²), 0<I< 3 f(x) = 0,…

A: From the given information, fx=1121+x2, 0&lt;x≤3 Y=3X+1 i) The distribution function of Y: Hy=PY≤y…

Q: The probability density function of a continuous random variable is: 4 (1+x) if -1 < x < 0 x < 0) 5…

A: From the given information, fx=451+x, if -1&lt;x&lt;04153-2x, if 0≤x&lt;32   For -1&lt;x&lt;0,…

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

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Q: Let X be a continuous random variable with probability density function 2x f(x; 0) for x > 0 (and…

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Q: Example-1: Suppose a continuous random variable X has the following probability density eX, x > 0…

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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!