Find the expected value and variance of the random variableX whose density function is f(x) = 1/(2(x)^0.5), 1 ≤ x ≤ 4.

Q: 10) Let f(x) by the probability density function of some continuous random variable. Explain why it…

A: If f(x) denotes the probability density function of some continuous random variable where x goes to…

Q: Let X be a random variable with pdf f(x) = kx*,-1 <x< 1. Find E (X).

A:

Q: Normal distribution.   The moment generating function of a random variable U is M(t) = (1 -…

A:

Q: The weekly demand for propane gas (in 100's of gallons) from a particular facility is a random…

A:

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: Prove that if M(t) is the MGF of a random variable X, then the MGF of a + bX is e^at M (bt)

A:

Q: Let xyz be the random quantities of three standard normal distributions, corr(X,Y) = 0.3, corr(X,Z)…

A: Given information: It is given that X, Y, Z are random quantities of three standard normal…

Q: the pdf of a random variable x is given by f(x;θ) = θx^θ−1 x ∈ (0,1). find the maximum likelihood…

A: The likelihood and log likelihood functions are as follows:

Q: The lengths of phone calls (in minutes) made by travel agent can be modeled as a continuous random…

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

Q: Let X be a continuous random variable with density f (x) = 24x-4 for æ > 2. Then Var (X) is equal to

A:

Q: The amount of time required to serve a customer at a bank has an exponential density function with a…

A: Given: Exponential pdf is as fx=ke-kx   0&lt;x&lt;∞ Mean = 3

Q: X is a uniform random variable with expected value μx = 7 and variance Var[X] = 3. What is the PDF…

A: The objective of the question is to find the Probability Density Function (PDF) of a uniform random…

Q: Let  X ~ Bernoulli (p). let Y be some discrete random variable. Know that Y is independent of X.…

A: Let X ~ Bernoulli (p) .Then E(X) = p and V(X) = p (1-p).

Q: Let Y₁, Y₂,. density function " Yn denote a random sample from a uniform distribution with 1, 0 ≤ y…

A: The objective of this question is to show that the α-level Likelihood Ratio Test (LRT) for a uniform…

Q: Let X1, X2, ..., Xn be a random sample from a Uniform(0,0 + 1) population with 0 > 0, *(3)**(3+1) X…

A: Given that, Let X1,X2,...,Xnbe a random sample from a uniform θ,θ+1population with θ&gt;0 where n is…

Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

A:

Q: The probability density function of the random variable X is given by 3 a2, 0< < 2 f(x) = otherwise…

A:

Q: Find the variance for g(X) = 3X* +2

A: Given f(x), we need to variance of g(X)

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

A: