random variable X has a PDF f(x)=C(8*x−x^2) for 0

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Q: Derive the variance of the Student's t distribution using the definition Var (X) = ELX²] - Ex)²

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Q: continuous random Variable X has probability Density function defined by f(x) = 5-5x;  0

A: Given: f(x) = 5-5x

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A: For the given random variable X, its pdf is

Q: 6. The pH water samples from a specific lake is a random variable X with probability density…

A: a) fx=387-x2, 5≤x≤7 EX=∫57xfxdx       =∫57x*387-x2dx      =38*443      =112

Q: Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard…

A: GivenMean(μ)=25standard deviation(σ)=4

Q: X is distributed as a Normal random variable with mean of 100 and a standard deviation of 10 (i.e…

A: Given information- We have given that- X ~ N (100,10) Population mean, µ = 100 Sample size, n = 20…

Q: 2. Suppose that a continuous random variable X has PDF f(x) = }7 (1 – x²) -1<x<1 else

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Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

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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: let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance…

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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: The random variable x follows a uniform probability distribution in the interval (0,1); the…

A: We know that  The pdf of Uniform distribution is  f(x) = { 1/(b-a) ,   a&lt;x&lt;b                0.…

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Q: (a)Find the probability that the selected bulb can survive for at least 3 years. (b)Find the…

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Q: If the variance of a continuous random variable X with pdf f(x) is noted as V(X), what is its…

A: Given: X had pdf f(x) and Variance of random variable X is - V(X)

Q: If X ∼ Gamma(2, 5), find E(X^2 ) andE(X^4 )

A: Solution: Let X follows gamma distribution with the parameters 2 and 5.

Q: Find the standard deviation of a discrete random variable X which satisfies P(X=1)=0.1,P(X=-1)=0.6,…

A: Given: A discrete random variable X satisfies the following:     P(X=1)=0.1P(X=-1)=0.6    P(X=2)=0.3

Q: The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular…

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Q: 3- 3 f(r) = I = 0,1,2, 3.

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Q: 7. Let X be a continuous random variable with pdf f(x)=√ 0<x< 9. (a) Find c. (b) Find the mean and…

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Q: rva

A: To find the variance of the damage from a random hurricane.

Q: Suppose X is random variable with E(X^2)= 10 and E(X)=2. What is the variance of X? Suppose X is a…

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Q: Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation…

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Q: Determine the mean and the variance of X.

A: Given that  f(x) = 0.125 x    for 0&lt;x&lt;4   We know that  Mean = E(x) = ∫x.f(x) dx variance V(x)…

Q: A model for normal human body temperature, X, when measured orally in °F, is that it is normally…

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

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Q: Explain Functions of Normally and Log-normally Distributed Random Variables

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Q: True or False: For an exponentially distributed random variable, x, P(x) = 1/(b - a).

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Q: Q3/ consider a random variable X with density function 0.125(4+ 2x) 1< x < 2 f (x) 3D elsewhere Find…

A: From the given information, it is clear that, fx=0.1254+2x     1&lt;x&lt;20…