Find the mean of the random variable X with PDF S 3x² _if 0

Q: Let us consider a discrete random variable having the pmf given by, PX(k) = { (1/3) , k = 1   (2/3)…

A: The moment generating function of x is given by: Mxs=EesX=13es+23e2s+0e3sMxs=13es+23e2s

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Q: the moment generating function of the random variable is always exist

A: The moment generating function of a random variable x, Mx(t) always exists. or not?

Q: Let X be a continuous random variable with PDF, (ke* : fx(x) = : otherwise x>0.

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Q: In a certain country, the amount of annual rainfall (in tonnes per m) is modelled through a Gamma…

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Q: The time required to repair a machine is an exponentially distributed random variable with mean of…

A: Given: λ=0.5

Q: Let X,, X2- --, Xn be a random sample from a normal distribution with mean M and variance o Show…

A: The joint pdf of X1, X2, ....., Xn is given as follows: f(x1, X2, ....., xn)=12πσnexp-12σ2∑ixi-μ2…

Q: Suppose that X is a continous random variable taking value between 0 and 1 with the pdf f(x) = 2x.…

A: There is two different question So i am solving first

Q: value

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Q: Show that the random variable X = Z and Y = 2?. fact that they are statistically dependent. are…

A: Answer: Using the given data,

Q: Let X be a random variable with expectation E(X)=10 and variance var(X)=5. Which lower bound does…

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Q: Let X, X, ..., X, be independent random variables from a distribution |(0+1)x° for 0-1 with pdf…

A: # given random variable x with pdf  f(x)=(theta+1)*x^theta  :0&lt;x&lt;1  then to find maximum…

Q: Suppose that Y Еxponential() ~ and let X = exp{-Y/ß} be a new continuous random variable. If…

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Q: For an initial investment of 100, an investment yields returns of Xi  at the end of period i for…

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Q: If X is a continuous random variable, what is the value of X that will be exceeded 30% of the time,…

A: Solution: It is needed to find the value of X.

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

A: (As per the bartleby guidelines, for more than one question asked, only first one is to be solved.…

Q: What is the pdf of the sum of two random variables each of which each is a gamma distribution with…

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Q: The random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of…

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A: The given probability density function is: fx=0.25e-0.25x The general expression of a exponential…

Q: ntinuous random variable

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Q: Let x be a normally distributed continuous random variable with a mean of 280 and a standard…

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Q: Suppose that X and Y are independent exponential random variables with parameter lambda = 1. Let Z =…

A: Exponential distribution: A random variable X is said to have a exponential distribution with a…

Q: (a) Suppose that an electronic device has a life length X (in units of 1000 hours) which is…

A: Given: X denotes the life length of an electronic device such that             f(x) = e-x,   x&gt;0…

Q: Let Xi. X2 --- Xn be a random sample from the Poisson _ 8*e¯® distribution . with pmf fix;o)=. Find…

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Q: If X is a continuous random variable, what is the value of X that will be exceeded 30% of the time,…

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Q: Suppose that X,, X2,...,X, denotes a random sample from a Poison distribution with mean 2. Find the…

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Q: i) Let X,X2, be two identical independent distributed (iid)random variables ,each X- X2 having chi –…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: The X be a continuous random variable with cumulative distribution function 1 F(x) = 1 for x > 0…

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Q: Two Independent random samples of n observations are to be selected from each of two binomial…

A: Given: α=1-0.98=0.02E=0.05

Q: The time required to repair a machine is an exponentially distributed random variable with mean of…

A: A machine is exponentially distributed with mean 0.5 hour

Q: Let X1,..., X, be a random sample from a distribution with PDF f(x) = 2e-2* where 0. The…

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Q: Assume that X donotos the continuous random varlable with probability distribution of y & (A) and…

A: Basic probability

Q: 6) Allow a continuous probability distribution to be defined as f(x) = 4x³ for the range 0 SXS1.…

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Q: Suppose X₁,..., Xn are independent exp(X) random variables, where X is the rate parameter. Find…

A: Dear student,  According to Bartleby guidelines we can answer only one question at once. If you need…

Q: The amount of time it takes Susan to wait for the bus is continuous and uniformly distributed…

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Q: Suppose that n observations are chosen at random from a continuous pdf fY(y).  What is the…

A: Suppose that n observations are chosen at random from a continuous distribution with a PDF fY(y)…

Q: Let X and Y be random variables having the same distribution. Show that Cov(X +Y, X – Y) = 0. |

A: Given that  X and Y are same distribution thenE(X2)=E(Y2) , E(X)=E(Y) Show that Cov(X+Y,X-Y)=0

Q: The variance of a binomial distribution cannot exceed Or Let x be a binomially distributed random…

A: As per our guidelines, we are allowed to answer first question only. Thanks   Let n be the sample…

Q: The time to fly between New York City and Chicago is uniformly distributed with a minimum of 56…

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Q: 2. Let Y < Y, < Y; be the order statistic of a random sample of size 3 from the uniform distribution…

A: Y1&lt;Y2&lt;Y3 are three order statistics which follow a Uniform distribution with the…

Q: Let {Xi}ni be IID from Uniform(θ,0). Find the likelihood function and the MLE of θ

A: It is known that, Xi~ U(θ,0)  P.d.f. of uniform distribution, f(x)= 1/(θ-0) ;     0&lt;x&lt;θ = 1/θ…