Let the probability function of the random variable X be defined as f(x)=cx^4 for x > 1, otherwise f(x)=0. Calculate the constant c, the expected value and the variance.

Q: Show the derivation of the PDF of the student's T-Distribution. Show complete solution.

A: Drive the pdf of student's t distribution

Q: Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.

A:

Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34.…

A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

Q: If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean…

A: Solution: From the given information, the probability density function of X is

Q: Suppose that f (x) = e* for 0 < x Determine the mean and variance of the random variable.

A:

Q: Find the distribution function which corresponds to the probability distribution defined by f (x) =…

A:

Q: because all airline passengers do not show up their reserved seat, an airline sells n = 125 tickets…

A: Let X be the random variable representing the number of passengers, out of 125, showing up to board…

Q: Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and variance of x.

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: QUESTION 19 The graduates at a southern university are shown in the table. Art & Science Education…

A:

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

A:

Q: Let X be a random variable representing the number of times that you have to roll two dice until you…

A: Here, the given context follows negative binomial distribution with k = 10 and p = 118 (probability…

Q: Find the mean and variance for the probability distribution given by f(x)= 2x k(k+1)* -,x=1,2,3,...k

A:

Q: b) Find the variance Var(X) of X.

A:

Q: Suppose that the random change in value of a financial asset is X over the first day and Y over the…

A: The variance of X+Y is calculated asVarX+Y=VarX+VarY-2CovX,Y

Q: Find the probability distribution of the random variable y, which represents the number of times…

A: Given, Y 1 2 3 f(y) 130 430 930

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: The number of cracks that need repair in a section of interstate highway follows a Poisson…

A: For a discrete random variable X ~P(m) the pmf is given as :   P(X=x) = e-mmxx!      , x=0,1,2,3,...…

Q: Y, = XB + ɛ, Show that the model variance in model Yi unbiased estimator of

A:

Q: A freight company is shipping boxes that have an expected value of 2000 TL. The variance of the…

A: The expectation of a discrete random variable X, denoted by E(X), is defined as a measure of central…

Q: rva

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

Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

A:

Q: Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1 2.5). (b) Calculate the variance of Y…

A: Solution

Q: In the 2012 presidential election, exit polls from the critical state of Ohio provided the following…

A: As per our guidelines, we are allowed to answer first question only. Thanks   Given Data :

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: Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution

A: The geometric distribution and Poisson distribution are two different types of probability…

Q: Let X ~ Uniform(a, b). Find Expected value EX.

A: Given X~Uniform(a, b)

Q: The number of work accidents that occur per week in a mine follows Poisson's law so that the…

A: It is given that P(X = 2) =(3/2) P(X = 1). That is,

Q: Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1.  Calculate the mean(x)

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

A: calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution…

Q: let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2.…

A: Result: If X~N(0,1) then X2~χ2(1) χ2(n1)+χ2(n2)=χ2(n1+n2)  E(χ2(n))=n and V(χ2(n))=2n

Q: Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is

A: From the given information, the joint density function for X  and Y is,

Q: Let the random variable X be normally distributed with mean 6 and variance 4. (A) Find the…

A: Given data: Mean = 6 Variance = 4 Thus, Std. Dev = sqrt(variance) = sqrt(4) = 2

Q: The expectation of X, which is also known as the mean or average, is E(X) = 7 and the Variance of X…

A: We have given that  The expectation of X, which is also known as the mean or average, is E(X) = 7…

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!